Cheukting/mathqa huggingface dataset:
Question (general): 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
Question (gain): 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
Question (other): 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
Question (geometry): in right triangle abc , ac is the hypotenuse . if ac is 20 and ab + bc = 50 , what is the area of the triangle abc ?
Options: a ) 225 , b ) 525 , c ) 25 √ 2 , d ) 200 , e ) 200 √ 2
Rationale: "square ab + bc = 50 : ( ab ) ^ 2 + 2 * ab * bc + ( bc ) ^ 2 = 2500 . since ( ac ) ^ 2 = ( ab ) ^ 2 + ( bc ) ^ 2 = 20 ^ 2 = 400 , then ( ab ) ^ 2 + 2 * ab * bc + ( bc ) ^ 2 = 400 + 2 * ab * bc = 2500 . 400 + 2 * ab * bc = 2500 . ab * bc = 1050 . the area = 1 / 2 * ab * bc = 525 . answer : b ."
Answer: b
Question (geometry): 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
Question (geometry): 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
Question (general): 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
Question (general): 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
Question (general): 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
Question (gain): 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
Question (general): 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
Question (general): 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
Question (gain): 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
Question (general): 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
Question (general): 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
Question (general): 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
Question (general): 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
Question (general): 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
Question (general): 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
Question (general): 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
Question (gain): 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
Question (general): 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
Question (geometry): 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
Question (general): 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
Question (gain): 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
Question (other): 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
Question (general): 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
Question (gain): 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
Question (general): 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
Question (gain): 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
Question (other): 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
Question (gain): 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
Question (general): 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
Question (physics): 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
Question (physics): 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
Question (general): 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
Question (gain): 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
Question (other): 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
Question (general): 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
Question (gain): 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
Question (other): 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
Question (general): 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
Question (general): 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
Question (gain): 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
Question (general): 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
Question (general): 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
Question (physics): a can do a work in 6 days , b can do a work in 8 days and c can do it in 12 days . b left work after 3 days . for how many number of days should a and c should work together to complete the remaining work ?
Options: a ) 0.1 , b ) 0.2 , c ) 0.3 , d ) 0.4 , e ) 0.5
Rationale: "b work 1 / 8 * 3 = 3 / 8 remaining work = 1 - 3 / 8 = 5 / 8 a and c work together = 1 / 6 + 1 / 12 = 3 / 12 = 1 / 4 remaining work is done in = 8 / 5 * 1 / 4 = 2 / 5 = 0.4 answer : d"
Answer: d
Question (general): what is the greatest 6 - digit number when divided by 8 , 9 , and 10 leaves a remainder of 6 , 7 , and 8 respectively ?
Options: a ) 456780 , b ) 678918 , c ) 997479 , d ) 997916 , e ) 997920
Rationale: when you divide a positive integer by 10 , the remainder will just be the units digit . we know the remainder is 8 when we divide by 10 , so b is the only possible answer .
Answer: b
Question (physics): a thief is spotted by a policeman from a distance of 160 meters . when the policeman starts the chase , the thief also starts running . if the speed of the thief be 8 km / hr and that of the policeman 10 km / hr , how far the thief will have run before he is overtaken ?
Options: a ) 350 m , b ) 240 m , c ) 440 m , d ) 640 m , e ) none of them
Rationale: "relative speed of the policeman = ( 10 - 8 ) km / hr = 2 km / hr . time taken by police man to cover ( 160 m / 1000 ) x 1 / 2 hr = 2 / 25 hr . in 2 / 25 hr / s , the thief covers a distance of 8 x 2 / 25 km = 16 / 25 km = 640 m answer is d ."
Answer: d
Question (general): the average of runs of a cricket player of 20 innings was 36 . how many runs must he make in his next innings so as to increase his average of runs by 4 ?
Options: a ) 96 , b ) 106 , c ) 122 , d ) 116 , e ) 120
Rationale: "average = total runs / no . of innings = 36 so , total = average x no . of innings = 36 * 20 = 720 now increase in avg = 4 runs . so , new avg = 36 + 4 = 40 runs total runs = new avg x new no . of innings = 40 * 21 = 840 runs made in the 11 th inning = 840 - 720 = 120 answer : e"
Answer: e
Question (general): the product of a and b is equal to 14 more than twice the sum of a and b . if b = 8 , what is the value of b - a ?
Options: a ) 2 , b ) 3 , c ) 7 , d ) 24 , e ) 35
Rationale: "ab = 14 + 2 ( a + b ) 8 a = 14 + 2 a + 16 6 a = 30 a = 5 b - a = 8 - 5 = 3 b is the answer"
Answer: b
Question (physics): excluding stoppages , the speed of a train is 42 kmph and including stoppages it is 36 kmph . of how many minutes does the train stop per hour ?
Options: a ) 7.5 , b ) 8.5 , c ) 9.5 , d ) 4.5 , e ) 6.5
Rationale: t = 6 / 42 * 60 = 8.5 answer : b
Answer: b