euclaise/mathqa_programs huggingface dataset:
Problem: the distance between delhi and mathura is 110 kms . a starts from delhi with a speed of 20 kmph at 7 a . m . for mathura and b starts from mathura with a speed of 25 kmph at 8 p . m . from delhi . when will they meet ?
Options: a ) 08 a . m . , b ) 09 a . m . , c ) 12 a . m . , d ) 10 a . m . , e ) 07 a . m .
Rationale: "d 10 a . m . d = 110 – 20 = 90 rs = 20 + 25 = 45 t = 90 / 45 = 2 hours 8 a . m . + 2 = 10 a . m ."
Answer: d
Python program:
a = 20 + 25 
b = 110 / a
c = 8 + b
Problem: how many positive integers less than 100 are neither multiples of 3 or 4 .
Options: a ) a ) 50 , b ) b ) 31 , c ) c ) 32 , d ) d ) 33 , e ) e ) 34
Rationale: "to answer this q we require to know 1 ) multiples of 3 till 100 = 100 / 3 = 33 2 ) multiples of 4 till 100 = 100 / 4 = 25 add the two 25 + 33 = 58 ; subtract common terms that are multiple of both 3 and 4 . . lcm of 4 and 3 = 12 multiples of 6 till 100 = 100 / 12 = 8.3 = 8 so total multiples of 3 and 4 = 58 - 8 = 50 ans = 100 - 50 = 50 a"
Answer: a
Python program:
a = 4 + 3 
b = a - 1
c = math.factorial(b)
d = math.factorial(3)
e = 4 - 1
f = math.factorial(e)
g = d * f
h = c / g
Problem: shopkeeper rise price by 31 % and gives successive discount of 10 % and 15 % . what is overall % gain or loss ?
Options: a ) 0.215 % , b ) 1.215 % , c ) 3.215 % , d ) 6.215 % , e ) 7.215 %
Rationale: "let d initial price be 100 31 % rise now price = 131 / 100 * 100 = 131 10 % discount then price = 131 * 90 / 100 = 117.9 15 % discount then price = 117.9 * 85 / 100 = 100.215 so gain = 100.215 - 100 = 0.215 gain % = gain * 100 / cp = = > 0.215 * 100 / 100 = 0.215 % answer : a"
Answer: a
Python program:
a = 100 + 31 
b = 100 - 10
c = b / 100
d = a * c
e = 100 - 15
f = e / 100
g = d * f
h = g - 100
Problem: the probability that a computer company will get a computer hardware contract is 4 / 5 and the probability that it will not get a software contract is 3 / 5 . if the probability of getting at least one contract is 9 / 10 , what is the probability that it will get both the contracts ?
Options: a ) 1 / 8 , b ) 2 / 9 , c ) 3 / 10 , d ) 4 / 11 , e ) 5 / 12
Rationale: "let , a ≡ event of getting hardware contract b ≡ event of getting software contract ab ≡ event of getting both hardware and software contract . p ( a ) = 4 / 5 , p ( ~ b ) = 5 / 9 = > p ( b ) = 1 - ( 3 / 5 ) = 2 / 5 . a and b are not mutually exclusive events but independent events . so , p ( at least one of a and b ) = p ( a ) + p ( b ) - p ( ab ) . = > 9 / 10 = ( 4 / 5 ) + ( 2 / 5 ) - p ( ab ) . = > p ( ab ) = 3 / 10 . hence , the required probability is 3 / 10 . the answer is c ."
Answer: c
Python program:
a = 3 / 0
b = 4 / 5
c = 1 - b
d = a + c 
e = 5 / 10
f = d - e
Problem: a small , rectangular park has a perimeter of 560 feet and a diagonal measurement of 500 feet . what is its area , in square feet ?
Options: a ) 12,000 , b ) 19,600 , c ) 20,000 , d ) 20,400 , e ) 20,800
Rationale: "you can avoid a lot of work in this problem by recognizing that , with the info provided , the diagonal forms a triangle inside the rectangle with sides that have a 3 : 4 : 5 ratio . diagonal = 200 2 x + 2 y = 560 , or x + y = 280 a ^ 2 + b ^ 2 = c ^ 2 for each the sides of the triangle using the ratio 3 : 4 : 5 for sides , and knowing c = 500 , you can deduce the following a = 300 b = 400 300 x 400 = 120,000 a is the answer ."
Answer: a
Python program:
a = 2 + 3 
b = 500 / a
c = b * 3
d = 2 + 3 
e = 500 / d
f = e * 4
g = c * f
Problem: if k and w are the dimensions of a rectangle that has area 21 , and if k and w are integers such that k > w , what is the total number of possible values of k ?
Options: a ) two , b ) three , c ) four , d ) five , e ) six
Rationale: "kw = 21 = 21 * 1 = 7 * 3 - - > k can take 2 values , answer : a"
Answer: a
Python program:
a = 3 * 1
Problem: how many digits are in the number 50 ^ 8 × 8 ^ 3 × 11 ^ 2 x 10 ^ 6 ?
Options: a ) 22 , b ) 20 , c ) 19 , d ) 18 , e ) 17
Rationale: "whenever you are asked to find the number of digits , try to bring the number in multiples of 10 . this way , we can wasily calculate the umber of 0 ' s through the powers of 10 50 ^ 8 × 8 ^ 3 × 11 ^ 2 x 10 ^ 6 = ( 5 ^ 2 * 2 ) ^ 8 * 2 ^ 9 * 11 ^ 2 x 10 ^ 6 = 5 ^ 16 * 2 ^ 17 * 11 ^ 2 x 10 ^ 6 = 2 * 11 ^ 2 * 10 ^ 16 x 10 ^ 6 = 242 * 10 ^ 22 hence we would have 16 trailing 0 ' s and the three digits from 242 total digits = 3 + 22 = 25 correct option : e"
Answer: e
Python program:
a = 10 * 2
b = a - 2
Problem: the value of a scooter depreciates in such a way that its value of the end of each year is 3 / 4 of its value of the beginning of the same year . if the initial value of the scooter is rs . 40,000 , what is the value at the end of 4 years ?
Options: a ) 3277 , b ) 2977 , c ) 12656 , d ) 6077 , e ) 17112
Rationale: "explanation : 40,000 * ( 3 / 4 ) ^ 4 answer : c"
Answer: c
Python program:
a = 100 * 100
b = 4 * a
c = 3 / 4
d = c ** 4
e = b * d
Problem: the simple interest on a sum of money will be rs . 400 after 10 years . if the principal is trebled after 5 years what will be the total interest at the end of the tenth year ?
Options: a ) 800 , b ) 3799 , c ) 1200 , d ) 2693 , e ) 1732
Rationale: "p - - - 10 - - - - 400 p - - - 5 - - - - - 200 3 p - - - 5 - - - - - 600 - - - - - - = > 800 answer : a"
Answer: a
Python program:
a = 400 / 10
b = a * 5
c = b * 3
d = 400 / 10
e = d * 5
f = c + e
Problem: the banker â € ™ s gain on a sum due 3 years hence at 10 % per annum is rs . 120 . the banker â € ™ s discount is
Options: a ) rs . 960 , b ) rs . 840 , c ) rs . 520 , d ) rs . 760 , e ) none
Rationale: "solution t . d = ( b . g x 100 / r x t ) = rs . ( 120 x 100 / 10 x 3 ) = rs . 400 . b . d = rs ( 400 + 120 ) = rs . 520 . answer c"
Answer: c
Python program:
a = 120 * 100
b = 3 * 10
c = a / b
d = c + 120
Problem: when greenville state university decided to move its fine arts collection to a new library , it had to package the collection in 20 - inch by 20 - inch by 15 - inch boxes . if the university pays $ 0.90 for every box , and if the university needs 3.06 million cubic inches to package the collection , what is the minimum amount the university must spend on boxes ?
Options: a ) $ 255 , b ) $ 275 , c ) $ 459 , d ) $ 1,250 , e ) $ 2,550
Rationale: "total no . of boxes = 3060000 / ( 20 × 20 × 15 ) = 510 total cost = 510 × $ 0.9 = $ 459 answer c"
Answer: c
Python program:
a = 1000 * 1000
b = 3 * 6
c = 20 * 20
d = c * 15
e = b / d
f = e * 0
Problem: for any number y , y * is defined as the greatest positive even integer less than or equal to y . what is the value of 5.0 – 5.0 * ?
Options: a ) 0.2 , b ) 1.2 , c ) 1.8 , d ) 2.2 , e ) 1.0
Rationale: "since y * is defined as the greatest positive even integer less than or equal to y , then 5.0 * = 4 ( the greatest positive even integer less than or equal to 5.0 is 4 ) . hence , 5.0 – 5.0 * = 5.0 - 4 = 1.0 answer : e ."
Answer: e
Python program:
a = math.floor(5, 0)
b = a - 1
c = 5 - 0
Problem: the salary of a person was reduced by 10 % . by what percent should his reduced salary be raised so as to bring it at par with his original salary ?
Options: a ) 10 % , b ) 11 1 / 9 % , c ) 13 2 / 7 % , d ) 15 3 / 11 % , e ) 12 1 / 3 %
Rationale: "let the original salary be $ 100 new salary = $ 90 increase on 90 = 10 increase on 100 = 10 / 90 * 100 = 11 1 / 9 % answer is b"
Answer: b
Python program:
a = 10 / 100
b = 100 * a
c = 10 / 100
d = 100 * c
e = 100 - d
f = b / e
g = f * 100
Problem: if the average ( arithmetic mean ) of 102 consecutive odd integers is 414 , then the least of these integers is
Options: a ) a ) 160 , b ) b ) 289 , c ) c ) 250 , d ) d ) 313 , e ) e ) 525
Rationale: "a very helpful rule to know in arithmetic is the rule that in evenly spaced sets , average = median . because the average will equal the median in these sets , then we quickly know that the median of this set of consecutive odd integer numbers is 414 . there are 102 numbers in the set , and in a set with an even number of terms the median is just the average of the two most median terms ( here the 51 st and 52 nd numbers in the set ) . this means that numbers 51 and 52 in this set are 413 and 415 . because we know that number 51 is 413 , we know that the smallest number is 50 odd numbers below this , which means that it is 50 * 2 = 100 below this ( every odd number is every other number ) . therefore 413 - 100 = 313 , answer choice d"
Answer: d
Python program:
a = 414 - 102
b = a + 1
Problem: 10 play kabadi , 40 play kho kho only , 5 play both gmaes . then how many in total ?
Options: a ) 30 , b ) 35 , c ) 38 , d ) 40 , e ) 50
Rationale: "10 play kabadi = > n ( a ) = 10 , 5 play both gmaes . = > n ( anb ) = 5 40 play kho kho only , = > n ( b ) = n ( b only ) + n ( anb ) = 40 + 5 = 45 total = > n ( aub ) = n ( a ) + n ( b ) - n ( anb ) = 10 + 45 - 5 = 50 answer : e"
Answer: e
Python program:
a = 40 + 5 
b = 10 + a 
c = b - 5
Problem: set s consists of integers { 6 , 8 , 10 , 12 , 14 } . if integer n is included in the set , the average ( arithmetic mean ) of set s will increase by 30 % . what is the value of integer n ?
Options: a ) 10 , b ) 12 , c ) 16 , d ) 22 , e ) 28
Rationale: "the average of the numbers in set s is 10 . if we increase the mean by 30 % , the new mean is 13 . thus , on average , 5 numbers increase by 3 . therefore n = 13 + 15 = 28 the answer is e ."
Answer: e
Python program:
a = 10 + 12 
b = a + 12
Problem: 1 + 2 = 10 2 + 3 = 26 3 + 4 = 50 then 4 + 5 = ?
Options: a ) 80 , b ) 81 , c ) 82 , d ) 83 , e ) 84
Rationale: 1 + 2 = 10 . . . . . ( 1 + 2 ) ^ 2 + 1 = 10 2 + 3 = 26 . . . . . . . ( 2 + 3 ) ^ 2 + 1 = 26 3 + 4 = 50 then . . . ( 3 + 4 ) ^ 2 + 1 = 50 4 + 5 = 82 . . . . . . . . ( 4 + 5 ) ^ 2 + 1 = 82 answer : c
Answer: c
Python program:
a = 4 + 5 
b = a ** 2
c = b + 1
Problem: n is a positive integer . when n + 1 is divided by 4 , the remainder is 3 . what is the remainder when n is divided by 3 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 0 , e ) 4
Rationale: "n + 1 = 4 a + 3 i . e . n + 1 = 7 , 10 , 13 , 16 , . . . etc . i . e . n = 6 , 9 , 12 , 15 , . . . etc . when n is divided by 3 remainder is always 0 answer : d"
Answer: d
Python program:
a = 3 + 3 
b = 4 / a
Problem: in the list 3 , 4 , 5 , 5 , 5 , 5 , 7 , 11 , 21 , what fraction of the data is less than the mode ?
Options: a ) 2 / 9 , b ) 1 / 3 , c ) 2 / 5 , d ) 2 / 3 , e ) 7 / 9
Rationale: highest frequent term in the set is 5 ( with frequency 4 ) hence mode = 5 two terms ( 3 , 4 ) out of a total of 9 terms are less than mode of the set . fraction of set that are less than mode of set = 2 / 9 answer : option a
Answer: a
Python program:
a = 5 + 4 
b = 2 / a
Problem: how many multiples of 8 are less than 4500 , and also multiples of 12 ?
Options: a ) 104.6 , b ) 187.5 , c ) 625.6 , d ) 450.5 , e ) 467.4
Rationale: "lcm of 8 & 12 = 24 tried dividing 4500 by 24 got quotient 187.5 ' so b is answer"
Answer: b
Python program:
a = 12 - 4500
b = a / 8
c = b + 1
Problem: john makes $ 60 a week from his job . he earns a raise andnow makes $ 84 a week . what is the % increase ?
Options: a ) 16.12 % , b ) 16.66 % , c ) 16.56 % , d ) 40 % , e ) 18.1 %
Rationale: "increase = ( 24 / 60 ) * 100 = ( 4 / 10 ) * 100 = 40 % . d"
Answer: d
Python program:
a = 84 - 60
b = a / 60
c = b * 100
Problem: 56 is to be divided into two parts such that the sum of 10 times the first and 22 times the second is 780 . the bigger part is :
Options: a ) 33.0 , b ) 37.66 , c ) 32.1 , d ) 31.23 , e ) 19
Rationale: explanation : let the two parts be ( 56 - x ) and x . then , 10 ( 56 - x ) + 22 x = 780 = > 12 x = 220 = > x = 20 . bigger part = ( 56 - x ) = 37.66 . answer : b ) 37.66
Answer: b
Python program:
a = 56 * 10
b = 780 - a
c = 22 - 10
d = b / c
e = 56 - d
Problem: the sides of a cube measures 8 cm . if the surface area of the cube is the same as a ball , what is the radius of the ball ? round to the nearest whole number .
Options: a ) 3 , b ) 8 , c ) 7 , d ) 6 , e ) 5
Rationale: first calculate the surface area of the cube . the cube is made of 6 squares with the sides measuring 8 cm each . the surface area of 1 side of the cube is 64 cm . multiply the surface area of the 1 side by 6 will give you the cube ' s total surface area . the cubes total surface area is 384 cm . now we know that the surface area of the ball is 384 cm . to find out the surface area of a sphere you need to square the radius , then multiply by pi , and multiply by the number 4 . going backwards to find the radius - you will need to dived the surface area by 96 . then divide by pi . then determine the square root of the answer . the radius is 5.527 . rounding to the nearest whole number the radius is 6 . the correct answer is ( d ) .
Answer: d
Python program:
a = surface_cube / (
b = a / 4
c = math.sqrt(b)
d = math.floor(c)
Problem: find the value for x from below equation : x / 2 = - 2 ?
Options: a ) - 6 , b ) 1 , c ) - 2 , d ) - 3 , e ) - 4
Rationale: "1 . multiply both sides by 2 : x * 2 / 2 = - 2 / 2 simplify both sides : x = - 4 e"
Answer: e
Python program:
a = 2 - 4
b = a * 2
Problem: a man sold 18 toys for rs . 18900 , gaining thereby the cost price of 3 toy find the cost price of a toy
Options: a ) s . 600 , b ) s . 800 , c ) s . 500 , d ) s . 900 , e ) s . 990
Rationale: "let the cost of one toy = x . then , cost of 18 toys = 18 x . gain = 3 x . sp of 18 toys = rs . 18900 . gain = sp â € “ cp 3 x = 18900 â € “ 18 x 21 x = 18900 x = rs . 900 . answer : option d"
Answer: d
Python program:
a = 18 + 3 
b = 18900 / a
Problem: how many of the positive factors of 75 are not factors of 95 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "factors of 75 - 1 , 3 , 5 , 15 , 25 , 75 , factors of 95 - 1 , 5 , 19 , 95 , comparing both , we have three factors of 75 which are not factors of 95 - 3 , 15 , 25 , 75 , the answer is e"
Answer: e
Python program:
a = 95 / 75
Problem: q is as much younger than r as he is older than t . if the sum of the ages of r and t is 50 years , what is definitely the difference between r and q ’ s age ?
Options: a ) 1 year , b ) 2 years , c ) 25 years , d ) data inadequate , e ) none of these
Rationale: "explanation given that : 1 . the difference of age b / w r and q = the difference of age b / w q and t . 2 . sum of age of r and t is 50 i . e . ( r + t ) = 50 . question : r – q = ? . explanation : r – q = q – t ( r + t ) = 2 q now given that , ( r + t ) = 50 so , 50 = 2 q and therefore q = 25 . question is ( r – q ) = ? here we know the value ( age ) of q ( 25 ) , but we don ’ t know the age of r . therefore , ( r - q ) can not be determined . answer d"
Answer: d
Python program:
a = 50 / 2
Problem: if it is assumed that 62 percent of those who receive a questionnaire by mail will respond and 300 responses are needed , what is the minimum number of questionnaires that should be mailed ?
Options: a ) 400 , b ) 420 , c ) 480 , d ) 483.8 , e ) 600
Rationale: "minimum no of mail to be sent for getting 300 responses at 62 % = 300 / 0.62 = 483.8 option d"
Answer: d
Python program:
a = 62 / 100
b = 300 / a
Problem: what is the lowest positive integer that is divisible by 1 through 2 , inclusive ?
Options: a ) 2 , b ) 4 , c ) 8 , d ) 6 , e ) 1
Rationale: the integer should be divisible by : 1 and 2 . the least common multiple of these integers is lcm = 1 * 2 = 2 answer : a
Answer: a
Python program:
a = math.lcm(1, 2)
Problem: the cost price of an article is 64 % of the marked price . calculate the gain percent after allowing a discount of 12 % .
Options: a ) 37.5 % , b ) 38.5 % , c ) 42 % , d ) 27.5 % , e ) none
Rationale: "sol . let marked price = rs . 100 . then , c . p . = rs . 64 . s . p = rs . 88 . ∴ gain % = [ 24 / 64 * 100 ] % = 37.5 % . answer a"
Answer: a
Python program:
a = 100 - 12
b = a / 64
c = b - 1
d = c * 100
Problem: two vessels having volumes in the ratio 3 : 5 are filled with water and milk solutions . the ratio of milk and water in the two vessels are 1 : 2 and 3 : 2 respectively . if the contents of both the vessel are empties into a larger vessel , find the ratio of milk and water in the larger vessel .
Options: a ) 99 : 61
b ) 1 : 1
c ) 61 : 160
d ) 61 : 99
e ) 99 : 160
Rationale: vessel a = 300 gallons - - > milk = 100 , water = 200 ; vessel b = 500 gallons - - > milk = 300 , water = 200 ; vessel a + b = 800 gallons - - > milk = 400 , water 400 . the ratio = 400 / 400 - - > 1 : 1 answer : b
Answer: b
Python program:
a = 1 ** 3
Problem: the profit earned by selling an article for rs . 832 is equal to the loss incurred when the same article is sold for rs . 448 . what should be the sale price for making 30 % profit ?
Options: a ) 220 , b ) 230 , c ) 960 , d ) 832 , e ) 400
Rationale: "c . p . = rs . x . then , 832 - x = x - 448 2 x = 1280 = > x = 640 required s . p . = 130 % of rs . 640 = 130 / 100 * 640 = rs . 832 . d"
Answer: d
Python program:
a = 832 - 448
b = a / 2
c = 832 - b
d = 30 / 100
e = 1 + d 
f = c * e
Problem: each year for 4 years , a farmer increased the number of trees in a certain orchard by 1 / 4 of the number of trees in the orchard of the preceding year . if all of the trees thrived and there were 1250 trees in the orchard at the end of 4 year period , how many trees were in the orchard at the beginning of the 4 year period .
Options: a ) 513 , b ) 512 , c ) 517 , d ) 519 , e ) 521
Rationale: trees increase by 1 / 4 the number of trees in preceding year . hence , correct answer must be divisible by 4 . based on divisibility rules , if last 2 digits are divisible by 4 then the number is divisible by 4 . thus , we can eliminate a , c , d , e the answer to be b again , trees increase by 1 / 4 the number of trees in preceding year . hence , the number of trees increase by 5 / 4 times the number of trees the preceding year . if x = initial number of trees = 512 year 1 = 5 / 4 x year 2 = ( 5 / 4 ) ( 5 / 4 ) x year 3 = ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) x year 4 = ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) x only for answer d : ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) 512 = 1250 hence , correct answer = b
Answer: b
Python program:
a = 1 / 4
b = a + 1 
c = b ** 4
d = 1250 / c
Problem: a river boat leaves silver town and travels upstream to gold town at an average speed of 6 kilometers per hour . it returns by the same route at an average speed of 5 kilometers per hour . what is the average speed for the round - trip in kilometers per hour ?
Options: a ) 5.5 , b ) 7.1 , c ) 7.2 , d ) 7.0 , e ) 8.0
Rationale: "pick a number which is lcm of 5 and 6 = 30 . upstream time = 30 / 6 = 5 hrs downstream time = 30 / 5 = 6 hrs total time = 11 hrs total distance = 60 average speed = 60 / 11 = 5.5 km / hr"
Answer: a
Python program:
a = 6 * 5
b = a * 2
c = 6 + 5 
d = b / c
Problem: a cistern is normally filled in 10 hours but takes two hours longer to fill because of a leak in its bottom . if the cistern is full , the leak will empty it in ?
Options: a ) 33 , b ) 88 , c ) 60 , d ) 99 , e ) 11
Rationale: "1 / 10 - 1 / x = 1 / 12 x = 60 answer : c"
Answer: c
Python program:
a = 1 / 10
b = 10 + 2 
c = 1 / b
d = a - c
e = 1/(d)
Problem: three numbers are in the ratio 4 : 5 : 6 and their average is 42 . the largest number is :
Options: a ) 28 , b ) 32 , c ) 36 , d ) 50.4 , e ) 45
Rationale: "explanation : let the numbers be 4 x , 5 x and 6 x . therefore , ( 4 x + 5 x + 6 x ) / 3 = 42 15 x = 126 x = 8.4 largest number = 6 x = 50.4 . answer d"
Answer: d
Python program:
a = 4 * 6
b = a * 100
c = 5 * 6
d = b + c
Problem: 6 % of customers that enter a store on any given day must not pay tax . if 1000 people shop every day , how many people pay taxes in the store every week
Options: a ) 6500 , b ) 6580 , c ) 7200 , d ) 7120 , e ) 6800
Rationale: 6 % of customers do not pay taxes . 6 / 100 * 1000 customers do not pay taxes . 6 / 100 * 1000 = 60 therefore 1000 - 60 customers do pay taxes . 1000 - 60 = 940 940 * 7 days per week = 6580 b )
Answer: b
Python program:
a = 6 + 1 
b = 6 / 100
c = 1000 * b
d = 1000 - c
e = a * d
Problem: find the compound ratio of ( 2 : 3 ) , ( 5 : 3 ) and ( 2 : 5 ) is
Options: a ) 1 : 2 , b ) 2 : 3 , c ) 3 : 4 , d ) 4 : 9 , e ) 3 : 2
Rationale: "required ratio = 2 / 3 * 5 / 3 * 2 / 5 = 4 / 9 = 4 : 9 answer is d"
Answer: d
Python program:
a = 2 / 3
b = 2 / 3
c = 5 / 3
d = b * c
e = a * d
Problem: 1 = 5,2 = 10,3 = 253,4 = 254,5 = 255,6 = 256,7 = 257,8 = 258 then 10 = ?
Options: a ) 2 , b ) 255 , c ) 345 , d ) 445 , e ) 235
Rationale: "1 = 5,2 = 10,3 = 253,4 = 254,5 = 255,6 = 256,7 = 257,8 = 258 then 10 = ? 10 = 2 check the first eqn . answer : a"
Answer: a
Python program:
a = 4 + 2 
b = 4 + 2 
c = a * b
d = c * 10
e = 255 - 6
f = e - 1
g = f / 2
Problem: p and q started a business investing rs . 85,000 and rs . 30,000 respectively . in what ratio the profit earned after 2 years be divided between p and q respectively ?
Options: a ) 17 : 6 , b ) 17 : 0 , c ) 17 : 4 , d ) 17 : 2 , e ) 17 : 3
Rationale: "p : q = 85000 : 30000 = 17 : 6 . answer : a"
Answer: a
Python program:
a = 2 + 3 
b = a + 3 
c = 2 + 3 
d = c * 2
e = b * d
f = 2 + 3 
g = e + f 
h = 2 + 3 
i = h * 2
j = 3 * i
k = 2 + 3 
l = j + k 
m = g / l
Problem: a raz ' s company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales were up 7 percent from 1996 . if total revenues from car sales and truck sales in 1997 were up 1 percent from 1996 , what is the ratio of revenue from car sales in 1996 to revenue from truck sales in 1996 ?
Options: a ) 1 : 2 , b ) 4 : 5 , c ) 1 : 1 , d ) 3 : 2 , e ) 5 : 3
Rationale: a raz ' s company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales were up 7 percent from 1996 . 1996 - x - - - - - y - - - - - - - x + y 1997 - x 1 - - - - y 1 - - x 1 + y 1 x 1 = a * x . . . . . ( p ) y 1 = 1.07 * y . . . ( q ) x 1 + y 1 / x + y = 1.01 solve using p and q and find x / y
Answer: a
Python program:
a = 100 + 7 
b = a / 100
c = 100 + 1 
d = c / 100
e = b - d
f = 100 + 1 
g = f / 100
h = 100 - 11
i = h / 100
j = g - i
k = e / j
Problem: what is the units digit of 23 ^ 3 * 17 ^ 2 * 39 ^ 2 ?
Options: a ) 9 , b ) 7 , c ) 5 , d ) 3 , e ) 1
Rationale: "the units digit of 23 ^ 3 is the units digit of 3 * 3 * 3 = 27 which is 7 . the units digit of 17 ^ 2 is the units digit of 7 * 7 = 49 which is 9 . the units digit of 39 ^ 2 is the units digit of 9 * 9 = 81 which is 1 . the units digit of 7 * 9 * 1 = 63 is 3 . the answer is d ."
Answer: d
Python program:
a = math.factorial(23)
b = math.factorial(3)
c = a * b
d = math.factorial(23)
e = math.factorial(2)
f = d * e
g = c + f 
h = g / 23
Problem: three numbers are in the ratio 4 : 5 : 6 and their average is 20 . the largest number is :
Options: a ) 24 , b ) 32 , c ) 36 , d ) 42 , e ) 45
Rationale: "explanation : let the numbers be 4 x , 5 x and 6 x . therefore , ( 4 x + 5 x + 6 x ) / 3 = 20 15 x = 60 x = 4 largest number = 6 x = 24 . answer a"
Answer: a
Python program:
a = 4 * 6
b = a * 100
c = 5 * 6
d = b + c
Problem: a customer went to a shop and paid a total of $ 25 , out of which 90 cents was for sales tax on taxable purchases . if the tax rate was 6 % , then what was the cost of the tax free items ?
Options: a ) $ 8.50 , b ) $ 8.70 , c ) $ 9.10 , d ) $ 10.00 , e ) $ 10.40
Rationale: "the total cost was $ 25 . the tax was $ 0.90 let the original price of the taxable items = x given that tax rate = 6 % 0.06 x = 0.90 x = $ 15 the cost of the tax free items was $ 25 - $ 15 - $ 0.90 = $ 9.10 the answer is c ."
Answer: c
Python program:
a = 25 - 90
b = 6 * 2
c = a - b
Problem: 45 x ? = 60 % of 900
Options: a ) 16.2 , b ) 12 , c ) 5 , d ) 500 , e ) none
Rationale: "answer let 45 x a = ( 60 x 900 ) / 100 ∴ a = ( 60 x 9 ) / 45 = 12 correct option : b"
Answer: b
Python program:
a = 60 / 100
b = a * 900
c = b / 45
Problem: set s contains exactly 10 numbers and has an average ( arithmetic mean ) of 6.2 . if one of the numbers in set s is increased by 6 , while all other numbers remain the same , what is the new average of set s ?
Options: a ) 6.6 , b ) 6.7 , c ) 6.8 , d ) 6.85 , e ) 6.9
Rationale: "old set s - total is avg * no of elements = 6.2 * 10 = 62 if one number is increased by 6 then total increased to 62 + 6 = 68 new avg - 68 / 10 = 6.8 . hence answer is c ."
Answer: c
Python program:
a = 10 * 6
b = a + 6 
c = b / 10