euclaise/mathqa_programs huggingface dataset:
Problem: machine a can process 6000 envelopes in 3 hours . machines b and c working together but independently can process the same number of envelopes in 2.5 hours . if machines a and c working together but independently process 3000 envelopes in 1 hour , then how many hours would it take machine b to process 7000 envelopes .
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 60 / 7
Rationale: "you can either take the amount of work done as the same as karishma has done or take the work done by each in the same time . i will do the latter 1 . work done in 1 hr by a is 2000 envelopes 2 . work done in 1 hr by a and c is 3000 envelopes 3 . so work done in 1 hr by c is 1000 envelopes 4 . work done in 1 hr by b and c is 2400 envelopes 5 . so work done in 1 hr by b is 1400 envelopes 6 . so to process 7000 envelopes b will take 7000 / 1400 hrs = 5 hrs so the answer is choice d"
Answer: d
Python program:
a = 6000 / 2
b = 3000 / 1
c = 6000 / 3
d = b - c
e = a - d
f = 7000 / e
Problem: abcd is a square aegf is a rectangle . . such that the rectangle shares 25 % of the area of the suare also ae lies on the line ab and ag lies on segment of ad . if the square shares half the area of the rectangle what is the ratio ae : ag ?
Options: a ) 1 : 4
b ) 8 : 1
c ) 4 : 1
d ) 3 : 1
e ) 1 : 3
Rationale: a - - - - - - - - - - - - b - - - - - - - - e | | 50 % | g - - - - - - - - - - - - | - - - - - - - - f | | | 75 % | d - - - - - - - - - - - c remaining square 75 % and remaining rectangle 50 % rectangle share 25 % area of square so , ab x ag = ( ad x ab ) / 4 ad = 4 ag - - - - - - - - - - - - - - - - - - ( 1 ) square share half the area of rectangle so , ag x ab = ( ae x ag ) / 2 ab = ae / 2 - - - - - - - - - - - - - - - - - - ( 2 ) in square all sides are equal i . e . ab = bc = cd = ad so , equation ( 1 ) and ( 2 ) both are equal ae / 2 = 4 ag ae / ag = 8 ae : ag = 8 : 1 answer : b
Answer: b
Python program:
a = 25 / 100
b = 1 / a
c = 1 / 2
d = b / c
Problem: 2 cow ’ s and 10 goats are brought for rs . 1500 . if the average price of a goat be rs . 70 . what is the average price of a cow .
Options: a ) 420 , b ) 400 , c ) 430 , d ) 410 , e ) 450
Rationale: "explanation : average price of a goat = rs . 70 total price of 8 goats = 10 * 70 = rs . 700 but total price of 2 cows and 8 goats = rs . 1500 total price of 2 cows is = 1500 - 700 = 800 average price of a cow = 800 / 2 = rs . 400 answer : b"
Answer: b
Python program:
a = 10 * 70
b = 1500 - a
c = b / 2
Problem: if x < y < z and y - x > 5 , where x is an even integer and y and z are odd integers , what is the least possible value f of z - x ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "x < y < z to find the least possible value for z - x ; we need to find the values for z and x that can be closest to each other . if x is some even number , then what could be minimum possible odd z . if x is some even number y - x > 5 ; y > x + 5 ; minimum value for y = x + 5 + 2 = x + 7 [ note : x + 5 is as even + odd = odd and nearest odd greater than x + 5 is x + 5 + 2 ] minimum value for z = y + 2 = x + 7 + 2 = x + 9 [ note : z = y + 2 because both z and y are odd . difference between two odd numbers is 2 ] f = z - x = x + 9 - x = 9 ans : d"
Answer: d
Python program:
a = 5 + 2 
b = a + 2
Problem: the ratio of males to females in a class is 2 : 3 . the career preferences of the students in the class are represented in a circle graph . if the area of the graph allocated to each career preference is proportional to the number of students who have that career preference , how many degrees of the circle should be used to represent a career that is preferred by two - thirds of the males and one - third of the females in the class ?
Options: a ) 160 , b ) 168 , c ) 191 , d ) 192 , e ) 204
Rationale: "2 / 3 * 2 / 5 + 1 / 3 * 3 / 5 = 4 / 15 + 3 / 15 = 7 / 15 the number of degrees is 7 / 15 * 360 = 168 degrees the answer is b ."
Answer: b
Python program:
a = 2 * 360
b = 2 + 3 
c = a / b
Problem: last year manfred received 26 paychecks . each of his first 6 paychecks was $ 750 ; each of his remaining paychecks was $ 60 more than each of his first 6 paychecks . to the nearest dollar , what was the average ( arithmetic mean ) amount of his pay checks for the year ?
Options: a ) $ 752 , b ) $ 796 , c ) $ 765 , d ) $ 773 , e ) $ 775
Rationale: "= ( 750 * 6 + 810 * 20 ) / 26 = 796 answer is b . posted from my mobile device"
Answer: b
Python program:
a = 750 + 60 
b = a * 60
c = 6 * 750
d = b + c 
e = d / 26
Problem: in the set of positive integers from 1 to 60 , what is the sum of all the odd multiples of 5 ?
Options: a ) 180 , b ) 185 , c ) 190 , d ) 160 , e ) 165
Rationale: 1 - 60 5 - 15 - 25 - 35 - 45 are valid multiples of 5 . add them 5 + 15 + 25 + 35 + 45 + 55 = 180 a
Answer: a
Python program:
a = 3 * 5
b = 60 * a
c = b / 5
Problem: a train is 360 meter long is running at a speed of 54 km / hour . in what time will it pass a bridge of 140 meter length ?
Options: a ) 65 seconds , b ) 33.33 seconds , c ) 40 seconds , d ) 97 seconds , e ) 26 seconds
Rationale: "speed = 54 km / hr = 54 * ( 5 / 18 ) m / sec = 15 m / sec total distance = 360 + 140 = 500 meter time = distance / speed = 500 * ( 1 / 15 ) = 33.33 seconds answer : b"
Answer: b
Python program:
a = 360 + 140 
b = 54 * 1000
c = b / 3600
d = a / c
Problem: if a certain number is divided by 12 , the quotient , dividend , and divisor , added together , will amount to 64 . what is the number ?
Options: a ) 18 , b ) 28 , c ) 48 , d ) 38 , e ) 59
Rationale: "let x = the number sought . then x / 12 + x + 12 = 64 . and x - 624 / 13 = 48 ."
Answer: a
Python program:
a = 64 - 12
b = a * 12
c = 12 + 1 
d = b / c
Problem: the ages of two persons differ by 24 years . if 5 years ago , the elder one be 5 times as old as the younger one , their present ages ( in years ) are respectively
Options: a ) 20,20 , b ) 20,10 , c ) 25,15 , d ) 35,11 , e ) none of these
Rationale: "explanation : let their ages be x and ( x + 24 ) years . 5 ( x - 5 ) = ( x + 24 - 5 ) or 4 x = 44 or x = 11 . their present ages are 35 years and 11 years option d"
Answer: d
Python program:
a = 24 * 5
b = 5 - 1
c = a / b
d = c + 5 
e = d - 24
Problem: what is the remainder when the number t = 14 ^ 2 * 15 ^ 8 is divided by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 4 , e ) 5
Rationale: "14 ^ 2 has units digit 6 15 ^ 8 has units digit 5 thus t = 14 ^ 2 * 15 ^ 8 has units digit 0 and will be divisible by 5 . the remainder will be zero answer : ( a )"
Answer: a
Python program:
a = 5 / 5
Problem: the monthly incomes of a and b are in the ratio 5 : 2 . b ' s monthly income is 12 % more than c ' s monthly income . if c ' s monthly income is rs . 15000 , then find the annual income of a ?
Options: a ) 187888 , b ) 276889 , c ) 267777 , d ) 504000 , e ) 297112
Rationale: "b ' s monthly income = 15000 * 112 / 100 = rs . 16800 b ' s monthly income = 2 parts - - - - > rs . 16800 a ' s monthly income = 5 parts = 5 / 2 * 16800 = rs . 42000 a ' s annual income = rs . 42000 * 12 = rs . 504000 answer : d"
Answer: d
Python program:
a = 12 / 100
b = 1 + a 
c = 15000 * b
d = 5 / 2
e = c * d
f = e * 12
Problem: if an article is sold at 18 % profit instead of 9 % profit , then the profit would be $ 72 more . what is the cost price ?
Options: a ) $ 500 , b ) $ 600 , c ) $ 700 , d ) $ 800 , e ) $ 900
Rationale: "9 % * cost price = $ 72 1 % * cost price = $ 72 / 9 = $ 8 the cost price is $ 800 . the answer is d ."
Answer: d
Python program:
a = 72 / 9
b = a * 100
Problem: by approximately what percent is x greater than 1 / 3 if ( 2 / 3 ) ( x ) = 1 ?
Options: a ) 173 % , b ) 516 % , c ) 461 % , d ) 350 % , e ) 290 %
Rationale: "what percent is x greater than 1 / 3 if ( 2 / 3 ) ( x ) = 1 ? = > x = 3 / 2 % change = [ ( 3 / 2 - 1 / 3 ) / ( 1 / 3 ) ] * 100 = 350 ans d , 350 %"
Answer: d
Python program:
a = 1 / 3
b = 3 - a
c = 1 / 3
d = b / c
e = d * 100
Problem: a train 1500 m long can cross an electric pole in 50 sec and then find the speed of the train ?
Options: a ) 106 , b ) 107 , c ) 108 , d ) 109 , e ) 110
Rationale: "length = speed * time speed = l / t s = 1500 / 50 s = 30 m / sec speed = 30 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 108 kmph answer : c"
Answer: c
Python program:
a = 1500 / 1000
b = 50 / 3600
c = a / b
Problem: in a certain company 20 % of the men and 40 % of the women attended the annual company picnic . if 35 % of all the employees are men . what % of all the employee went to the picnic ?
Options: a ) 33 % , b ) 34 % , c ) 35 % , d ) 36 % , e ) 37 %
Rationale: total men in company 35 % means total women in company 65 % ( assume total people in company 100 % ) no of men emplyess attended picnic = 35 x ( 20 / 100 ) = 7 no of women empolyees attened picnin = 65 x ( 40 / 100 ) = 26 total percentage of empolyess attened the picnic = 7 + 26 = 33 % answer : a
Answer: a
Python program:
a = 35 / 100
b = 20 / 100
c = a * b
d = 100 - 35
e = d / 100
f = 40 / 100
g = e * f
h = c + g 
i = h * 100
Problem: a rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 60 sq . feet , how many feet of fencing will be required ?
Options: a ) 34 , b ) 40 , c ) 68 , d ) 88 , e ) 26
Rationale: "we have : l = 20 ft and lb = 60 sq . ft . so , b = 3 ft . length of fencing = ( l + 2 b ) = ( 20 + 6 ) ft = 26 ft . answer : e"
Answer: e
Python program:
a = 60 / 20
b = a * 2
c = b + 20
Problem: if an integer w is to be chosen at random from the integers 1 to 96 , inclusive , what is the probability that w ( w + 1 ) ( w + 2 ) will be divisible by 8 ?
Options: a ) 1 / 4 , b ) 3 / 8 , c ) 1 / 2 , d ) 5 / 8 , e ) 3 / 4
Rationale: for w total numbers 8 * 12 there are 12 numbers divisible by 8 - > 3 * 12 ( if 8 is an example - ( 6 , 78 ) , ( 7 , 89 ) , ( 8 , 910 ) ) and 12 numbers divisible by 4 but not divisible by 8 - > 2 * 12 ( if 4 is an example ( 2 , 34 ) and ( 4 , 56 ) ) the answer 5 / 8 - > d
Answer: d
Python program:
a = 96 / 8
b = 96 / 2
c = a + b 
d = c / 96
Problem: tickets numbered from 1 to 24 are mixed and then a ticket is selected randomly . what is the probability that the selected ticket bears a number which is a multiple of 3 ?
Options: a ) 1 / 3 , b ) 2 / 5 , c ) 3 / 10 , d ) 3 / 7 , e ) 1 / 7
Rationale: here , s = [ 1 , 2 , 3 , 4 , … . , 19 , 20 , 21 , 22 , 23 , 24 ] let e = event of getting a multiple of 3 = [ 3 , 6 , 9 , 12 , 15 , 18 , 21 , 24 ] p ( e ) = n ( e ) / n ( s ) = 8 / 24 = 1 / 3 the answer is a .
Answer: a
Python program:
a = 24 / 3
b = a / 24
Problem: the difference of two numbers is 20 % of the larger number . if the smaller number is 12 , the larger one is :
Options: a ) 15 , b ) 16 , c ) 18 , d ) 20 , e ) none of these
Rationale: "let the larger number be x . then , x - 12 = 20 % of x < > x - ( x / 5 ) = 12 4 x / 5 = 12 < = > x = ( 12 ∗ 5 ) / 5 = 15 . answer : a"
Answer: a
Python program:
a = 10 / 2
b = a * 12
c = 10 / 2
d = c * 12
e = 20 + d 
f = e / 2
g = b - f
h = 10 / 2
i = g + h
Problem: sandy is younger than molly by 14 years . if their ages are in the respective ratio of 7 : 9 , how old is molly ?
Options: a ) 36 , b ) 45 , c ) 54 , d ) 63 , e ) 72
Rationale: "s = m - 14 s / m = 7 / 9 9 s = 7 m 9 ( m - 14 ) = 7 m m = 63 the answer is d ."
Answer: d
Python program:
a = 9 - 7
b = 7 / a
c = b * 14
Problem: carrie likes to buy t - shirts at the local clothing store . they cost $ 8.75 each . one day , she bought 18 t - shirts . how much money did she spend ?
Options: a ) $ 150 , b ) $ 70 , c ) $ 200 , d ) $ 171.6 , e ) $ 190
Rationale: $ 8.75 * 18 = $ 70 . answer is b .
Answer: b
Python program:
a = 18 * 8
b = math.floor(a)
Problem: a pharmaceutical company received $ 3 million in royalties on the first $ 20 million in sales of and then $ 8 million in royalties on the next $ 108 million in sales . by approximately what percentage did the ratio of royalties to sales decrease from the first $ 20 million in sales to the next $ 108 million in sales ?
Options: a ) 8 % , b ) 15 % , c ) 46 % , d ) 52 % , e ) 56 %
Rationale: "( 8 / 108 ) / ( 3 / 20 ) = 30 / 54 = 49,3 % it means that 8 / 108 represents only 49,3 % . therefore a decrease of 46 % . answer c"
Answer: c
Python program:
a = 3 / 20
b = a * 100
Problem: a group of 55 adults and 70 children go for trekking . if there is meal for either 70 adults or 90 children and if 14 adults have their meal , find the total number of children that can be catered with the remaining food .
Options: a ) 33 , b ) 54 , c ) 18 , d ) 17 , e ) 72
Rationale: "explanation : as there is meal for 70 adults and 14 have their meal , the meal left can be catered to 56 adults . now , 70 adults = 90 children 7 adults = 9 children therefore , 56 adults = 72 children hence , the meal can be catered to 72 children . answer : e"
Answer: e
Python program:
a = 70 - 14
b = 90 / 70
c = a * b
Problem: a batch of cookies was divided amomg 2 tins : 2 / 3 of all the cookies were placed in either the blue or the green tin , and the rest were placed in the red tin . if 1 / 4 of all the cookies were placed in the blue tin , what fraction of the cookies that were placed in the other tins were placed in the green tin
Options: a ) 15 / 2 , b ) 9 / 4 , c ) 5 / 11 , d ) 7 / 5 , e ) 9 / 7
Rationale: "this will help reduce the number of variables you have to deal with : g + b = 2 / 3 r = 1 / 2 b = 1 / 4 we can solve for g which is 5 / 12 what fraction ( let it equal x ) of the cookies that were placed in the other tins were placed in the green tin ? so . . x * ( g + r ) = g x * ( 5 / 12 + 1 / 2 ) = 5 / 12 x = 5 / 11 answer : c . 5 / 11"
Answer: c
Python program:
a = 2 / 3
b = 1 - a
c = 2 / 3
d = 1 / 4
e = c - d
f = b + e
Problem: robert ' s salary was decreased by 60 % and subsequently increased by 60 % . how much percentage does he lose ?
Options: a ) 10 % , b ) 20 % , c ) 25 % , d ) 36 % , e ) 50 %
Rationale: let original salary be $ 100 salary after decreasing 60 % = 100 - 100 x 60 / 100 = $ 40 salary after increasing 60 % on $ 40 = 40 + 40 x 60 / 100 = $ 64 percentage of loss = 100 - 64 = 36 % answer : d
Answer: d
Python program:
a = 100 * 100
b = 100 - 60
c = 100 + 60 
d = b * c
e = a - d
f = 100 * 100
g = e / f
h = g * 100
Problem: a candidate got 34 % of the votes polled and he lost to his rival by 640 votes . how many votes were cast ?
Options: a ) 2000 , b ) 2400 , c ) 2800 , d ) 3200 , e ) 3600
Rationale: "let x be the total number of votes . 0.34 x + 640 = 0.66 x 0.32 x = 640 x = 640 / 0.32 = 2000 the answer is a ."
Answer: a
Python program:
a = 34 / 100
b = 1 - a
c = 34 / 100
d = b - c
e = 640 / d
Problem: if x ¤ y = ( x + y ) ^ 2 - ( x - y ) ^ 2 . then √ 11 ¤ √ 11 =
Options: a ) 44 , b ) 5 , c ) 10 , d ) 15 , e ) 20
Rationale: x = √ 11 and y also = √ 11 applying the function ( √ 11 + √ 11 ) ^ 2 - ( √ 11 - √ 11 ) ^ 2 = ( 2 √ 11 ) ^ 2 - 0 = 4 x 11 = 44 . note : alternative approach is the entire function is represented as x ^ 2 - y ^ 2 = ( x + y ) ( x - y ) which can be simplified as ( x + y + x - y ) ( x + y - ( x - y ) ) = ( 2 x ) ( 2 y ) = 4 xy . substituting x = √ 11 and y = √ 11 you get the answer 44 . answer a
Answer: a
Python program:
a = math.sqrt(11)
b = math.sqrt(11)
c = a + b 
d = c ** 2
Problem: of the people who responded to a market survey , 200 preferred brand x and the rest preferred brand y . if the respondents indicated a preference for brand x over brand y by ratio of 4 to 1 , how many people responded to the survey ?
Options: a ) 80 , b ) 160 , c ) 250 , d ) 350 , e ) 480
Rationale: "ratio = 4 : 1 = > 4 x respondents preferred brand x and x preferred brand y since , no . of respondents who preferred brand x = 200 = > 4 x = 200 = > x = 50 hence total no . of respondents = 200 + 50 = 250 hence c is the answer ."
Answer: c
Python program:
a = 200 / 4
b = a + 200
Problem: 5358 x 55 = ?
Options: a ) 272258 , b ) 272358 , c ) 294690 , d ) 274258 , e ) 274358
Rationale: "5358 x 51 = 5358 x ( 50 + 5 ) = 5358 x 50 + 5358 x 5 = 267900 + 26790 = 294690 . c )"
Answer: c
Python program:
a = 5358 / 55
b = a * 100
Problem: the average of 5 numbers is 7.4 . if one of the numbers is multiplied by a factor of 3 , the average of the numbers increases to 9.2 . what number is multiplied by 3 ?
Options: a ) 1.5 , b ) 3.0 , c ) 3.9 , d ) 4.5 , e ) 6.0
Rationale: "the average of 5 numbers is 7.4 the sum of 5 numbers will be 7.4 x 5 = 37 the average of 5 number after one of the number is multiplied by 3 is 9.2 the sum of the numbers will now be 9.2 x 5 = 46 so the sum has increased by 46 - 37 = 9 let the number multiplied by 3 be n then , 3 n = n + 9 or 2 n = 9 or n = 4.5 answer : - d"
Answer: d
Python program:
a = 9 * 2
b = 7 * 4
c = a - b
Problem: the average marks obtained by 120 candidates in a certain examination is 35 . find the total marks .
Options: a ) 3800 , b ) 4500 , c ) 5200 , d ) 3400 , e ) 4200
Rationale: "following the above formula , we have the total marks = 120 * 35 = 4200 answer is e"
Answer: e
Python program:
a = 120 * 35
Problem: according to the directions on the can of frozen orange juice concentrate , 1 can of concentrate is to be mixed with 3 cans of water to make orange juice . how many 12 ounces cans of the concentrate are required to prepare 280 6 ounces servings of orange juice ?
Options: a ) a ) 35 , b ) b ) 34 , c ) c ) 50 , d ) d ) 67 , e ) e ) 100
Rationale: "its a . total juice rquired = 280 * 6 = 1680 ounce 12 ounce concentate makes = 12 * 4 = 48 ounce juice total cans required = 1680 / 48 = 35 . answer a"
Answer: a
Python program:
a = 280 * 6
b = a / 12
c = b / 4
Problem: a box contains either blue or red flags . the total number of flags in the box is an even number . a group of children are asked to pick up two flags each . if all the flags are used up in the process such that 60 % of the children have blue flags , and 45 % have red flags , what percentage of children have flags of both the colors ?
Options: a ) 5 % , b ) 10 % , c ) 15 % , d ) 20 % , e ) it can not be determined
Rationale: "solution : let the total number of flags be 100 ( even number ) let the total number of ' blue ' flags alone be ' a ' let the total number of ' red ' flags alone be ' b ' let the total number of ' both ' flags be ' c ' we have given , total number of blue flags = 60 % = 60 = a + c total number of red flags = 45 % = 45 = b + c total number of flags = a + b + c = 100 ( since all the flag have been utilized ) so , substituting for c in the third equation , we have , 60 - c + c + 45 - c = 100 c = 5 option a ."
Answer: a
Python program:
a = 60 + 45 
b = a - 100
Problem: if the perimeter of a rectangular playground is 1200 m , its length when its breadth is 500 m is ?
Options: a ) 300 , b ) 200 , c ) 100 , d ) 400 , e ) 500
Rationale: 2 ( l + 500 ) = 1200 = > l = 100 m answer : c
Answer: c
Python program:
a = 1200 / 2
b = a - 500
Problem: a doctor prescribed 18 cubic centimeters of a certain drug to a patient whose body weight was 115 pounds . if the typical dosage is 2 cubic centimeters per 15 pounds of the body weight , by what percent was the prescribed dosage greater than the typical dosage ?
Options: a ) 8 % , b ) 9 % , c ) 11 % , d ) 12.5 % , e ) 13.03 %
Rationale: "typical dosage is dose : weight : : 2 : 15 . now if weight is 115 : ( 115 / 15 ) ) then typical dosage would be 2 * 7.67 = 15.33 cc . dosage = 18 cc . dosage is greater by 2 cc . % dosage is greater : ( 2 / 15.33 ) * 100 = 13.03 % e is the answer ."
Answer: e
Python program:
a = 2 / 15
b = a * 115
c = b - 18
d = 2 / 15
e = d * 115
f = c / e
g = f * 100
Problem: what is the average ( arithmetic mean ) of all multiples of 10 from 10 to 500 inclusive ?
Options: a ) 190 , b ) 255 , c ) 200 , d ) 205 , e ) 210
Rationale: this question can be solved with the average formula and ' bunching . ' we ' re asked for the average of all of the multiples of 10 from 10 to 500 , inclusive . to start , we can figure out the total number of terms rather easily : 1 ( 10 ) = 10 2 ( 10 ) = 20 . . . 50 ( 10 ) = 500 so we know that there are 50 total numbers . we can now figure out the sum of those numbers with ' bunching ' : 10 + 500 = 510 20 + 490 = 510 30 + 480 = 510 etc . since there are 50 total terms , this pattern will create 25 ' pairs ' of 510 . thus , since the average = ( sum of terms ) / ( number of terms ) , we have . . . ( 25 ) ( 510 ) / ( 50 ) = 255 final answer : b
Answer: b
Python program:
a = 10 + 500 
b = 500 - 10
c = b / 10
d = c + 1 
e = a * d
f = e / 2
g = 500 - 10
h = g / 10
i = h + 1 
j = f / i
Problem: 64 ã — 64 ã — 64 ã — 64 x 64 = 8 ^ ?
Options: a ) 4 , b ) 7 , c ) 8 , d ) 10 , e ) none of these
Rationale: "64 ã — 64 ã — 64 ã — 64 x 64 = 8 ^ ? or , 8 ( 2 ) ã — 8 ( 2 ) ã — 8 ( 2 ) ã — 8 ( 2 ) x 8 ( 2 ) = 8 ? or 7 ( 10 ) = 8 ? or , ? = 10 answer d"
Answer: d
Python program:
a = 64 / 64
b = a - 1
Problem: a person can swim in still water at 4 km / h . if the speed of water 2 km / h , how many hours will the man take to swim back against the current for 14 km ?
Options: a ) 3 , b ) 6 , c ) 8 , d ) 9 , e ) 7
Rationale: m = 4 s = 2 us = 4 - 2 = 2 d = 14 t = 14 / 2 = 7 answer : e
Answer: e
Python program:
a = 4 - 2
b = 14 / a
Problem: find the sum the difference between the compound and s . i . on a certain sum of money for 2 years at 10 % per annum is rs . 15 of money ?
Options: a ) 1500 , b ) 2677 , c ) 1997 , d ) 2677 , e ) 1971
Rationale: p = 15 ( 100 / 10 ) 2 = > p = 1500 answer : a
Answer: a
Python program:
a = 10 * 2
b = 15 / a
c = b * 100
d = 10 * 2
e = c * d
Problem: one bottle is half - full of oil and another bottle with twice the capacity is one quarter full of oil . if water is added so that both the bottles are full and the contents of both are then poured into a third bottle that is empty and large enough to hold the contents of both , what fractions of the contents in the third bottle is oil ?
Options: a ) 1 / 4 , b ) 1 / 3 , c ) 3 / 8 , d ) 2 / 3 , e ) 1 / 2
Rationale: let assume that 1 st bottle capacity = 1 litre ; therefore , it contain 1 / 2 litre oil and 1 / 2 litre water . ( i . e ) water = 1 / 2 litre oil = 1 / 2 litre 2 nd bottle is twice the capacity i . e . 2 litre capacity it means , 1 / 2 litre filled with oil and 1 ( 1 / 2 ) litre filled with water . i . e . oil = 1 / 2 liter water = 1 ( 1 / 2 ) litre in total the third bottle will contain , 1 litre oil and 2 litre water . i . e . , oil = 1 litre water = 2 liter therefore , oil proportion is 1 / 3 answer : b
Answer: b
Python program:
a = 1 / 2
b = 2 / 4
c = a + b 
d = 2 / 4
e = 2 - d
f = 1 / 2
g = 1 - f
h = e + g 
i = 1 / 2
j = 2 / 4
k = i + j 
l = h + k 
m = c / l
Problem: a box contains 12 pairs of shoes ( 24 shoes in total ) . if two shoes are selected at random , what it is the probability that they are matching shoes ?
Options: a ) 1 / 190 , b ) 1 / 23 , c ) 1 / 19 , d ) 1 / 10 , e ) 1 / 9
Rationale: "the problem with your solution is that we do n ' t choose 1 shoe from 24 , but rather choose the needed one after we just took one and need the second to be the pair of it . so , the probability would simply be : 1 / 1 * 1 / 23 ( as after taking one at random there are 23 shoes left and only one is the pair of the first one ) = 1 / 23 answer : b"
Answer: b
Python program:
a = 24 - 1
b = 1 / a
Problem: if 2 ^ 5 , 3 ^ 3 , and 10 ^ 2 are all factors of the product of 936 and w where w is a positive integer , what is the smallest possible value of w ?
Options: a ) 26 , b ) 39 , c ) 120 , d ) 65 , e ) 156
Rationale: "here 156 has three two ' s two three ' s and one 10 rest of them must be in w so w = 10 * 3 * 4 = 120 smash c"
Answer: c
Python program:
a = 2 ** 2
b = a * 3
c = 10 / 2
d = b * c
e = d * 2
Problem: how long does a train 130 m long running at the speed of 65 km / hr takes to cross a bridge 150 m length ?
Options: a ) 15.7 sec , b ) 15.1 sec , c ) 15.5 sec , d ) 17.1 sec , e ) 16.7 sec
Rationale: "speed = 65 * 5 / 18 = 18.1 m / sec total distance covered = 130 + 150 = 280 m . required time = 280 / 18.1 ' = 15.5 sec . answer : c"
Answer: c
Python program:
a = 130 + 150 
b = 65 * const_0_2778
c = a / b