Cheukting/mathqa huggingface dataset:
Question (physics): a man can row downstream at 18 kmph and upstream at 16 kmph . find the speed of the man in still water and the speed of stream respectively ?
Options: a ) 13 , 3 , b ) 12 , 6 , c ) 15 , 3 , d ) 14 , 4 , e ) 17 , 1
Rationale: "explanation : let the speed of the man in still water and speed of stream be x kmph and y kmph respectively . given x + y = 18 - - - ( 1 ) and x - y = 16 - - - ( 2 ) from ( 1 ) & ( 2 ) 2 x = 34 = > x = 17 , y = 1 . answer : option e"
Answer: e
Question (gain): after giving a discount of rs . 45 the shopkeeper still gets a profit of 20 % , if the cost price is rs . 180 . find the markup % ?
Options: a ) 0.4 , b ) 0.55 , c ) 0.45 , d ) 0.48 , e ) 0.58
Rationale: cost price = 180 s . p = 180 * 120 / 100 = 216 disc = 45 so . . . mark price = 216 + 45 = 261 . . . . . . mark up % = 261 - 180 / 180 = 81 / 180 = . 45 or 45 % answer : c
Answer: c
Question (general): if x , y , and z are positive integers and 3 x = 2 y = 4 z , then the least possible value of x + y + z is
Options: a ) 15 , b ) 25 , c ) 30 , d ) 42 , e ) 13
Rationale: "given 3 x = 2 y = 4 z x + y + z in terms of x = x + ( 3 x / 2 ) + ( 3 x / 4 ) = 26 x / 8 = 13 x / 4 now checking with each of the answers and see which value gives a minimum integer value . a x = 4 / 13 * 15 , not an integer b , c , e can be ruled out similarly . d is minimum value as x = 13 * 4 / 13 = 4 answer is e"
Answer: e
Question (physics): a train travelling 80 kmph to pass through a tunnel of 70 km at 5 : 12 am . the train leaves the tunnel at 5 : 18 am . find the length of train ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: distance = speed * time let x is length of train 5 : 18 - 5 : 12 = 6 minutes = 6 / 60 hr = 1 / 10 hr now d = ( x + 7 ) = 80 kmph * 1 / 10 x = 1 km answer : a
Answer: a
Question (general): if x is equal to the sum of the integers from 30 to 50 , inclusive , and y is the number of even integers from 30 to 50 , inclusive , what is the value of x + y ?
Options: a ) 810 , b ) 811 , c ) 830 , d ) 850 , e ) 851
Rationale: since the integers from 30 - 50 are consecutive we can use the ` ` median x # of terms formula ' ' to determine x . there are 21 terms and the median is 40 . this gives a total of 21 x 40 = 840 . there are 11 even integers from 30 - 50 = y . therefore , x + y = 851 . answer : e
Answer: e
Question (general): of the 100 people in a room , 2 / 5 are women . if 1 / 4 of the people are married , what is the maximum number of women in the room who could be unmarried ?
Options: a ) 32 , b ) 34 , c ) 36 , d ) 38 , e ) 40
Rationale: women = 2 / 5 * 100 = 40 married = 1 / 4 * 100 = 25 unmarried = 75 max ( un - married women ) = 40 answer e
Answer: e
Question (physics): the length of the bridge , which a train 160 meters long and travelling at 45 km / hr can cross in 30 seconds , is :
Options: a ) 230 , b ) 244 , c ) 245 , d ) 215 , e ) 236
Rationale: "speed = ( 45 * 5 / 18 ) m / sec = ( 25 / 2 ) m / sec . time = 30 sec . let the length of bridge be x meters . then , ( 160 + x ) / 30 = 25 / 2 = = > 2 ( 160 + x ) = 750 = = > x = 215 m . answer : option d"
Answer: d
Question (gain): yesterday ' s closing prices of 1,760 different stocks listed on a certain stock exchange were all different from today ' s closing prices . the number of stocks that closed at a higher price today than yesterday was 20 percent greater than the number that closed at a lower price . how many of the stocks closed at a higher price today than yesterday ?
Options: a ) 960 , b ) 726 , c ) 1,100 , d ) 1,320 , e ) 1,694
Rationale: "lets consider the below - the number of stocks that closed at a higher price = h the number of stocks that closed at a lower price = l we understand from first statement - > h + l = 1760 - - - - ( 1 ) we understand from second statement - > h = ( 120 / 100 ) l = > h = 1.2 l - - - - ( 2 ) solve eq ( 1 ) ( 2 ) to get h = 960 . a is my answer ."
Answer: a
Question (general): if a certain toy store ' s revenue in november was 2 / 5 of its revenue in december and its revenue in january was 1 / 5 of its revenue in november , then the store ' s revenue in december was how many times the average ( arithmetic mean ) of its revenues in november and january ?
Options: a ) 5 / 2 , b ) 10 / 3 , c ) 15 / 4 , d ) 25 / 3 , e ) 25 / 6
Rationale: "n = 2 d / 5 j = n / 5 = 2 d / 25 the average of november and january is ( n + j ) / 2 = 12 d / 25 / 2 = 6 d / 25 d is 25 / 6 times the average of november and january . the answer is e ."
Answer: e
Question (general): john was thrice as old as tom 6 years ago . john will be 3 / 2 times as old as tom in 6 years . how old is tom today ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14
Rationale: "j - 6 = 3 ( t - 6 ) , so j = 3 t - 12 j + 6 = 3 / 2 * ( t + 6 ) 2 j + 12 = 3 t + 18 2 ( 3 t - 12 ) + 12 = 3 t + 18 3 t = 30 t = 10 the answer is c ."
Answer: c
Question (general): a rainstorm increased the amount of water stored in state j reservoirs from 130 billion gallons to 160 billion gallons . if the storm increased the amount of water in the reservoirs to 60 percent of total capacity , approximately how many billion gallons of water were the reservoirs short of total capacity prior to the storm ?
Options: a ) 92 , b ) 85 , c ) 136.67 , d ) 140.67 , e ) 150
Rationale: "let total capacity be x we know 160 = 0.60 x x = 160 / 0.60 = 266.67 prior to storm , we had 130 bn gallons 266.67 - 130 = 136.67 answer : c"
Answer: c
Question (general): what is the 8 th digit to the right of the decimal point in the decimal equivalent of 73 / 11 ?
Options: a ) 1 , b ) 3 , c ) 4 , d ) 5 , e ) 2
Rationale: "73 / 11 = 6.6363 . . . . 63 is non - terminating repeating decimal . the 8 th digit to the right of decimal point will be 3 . answer b"
Answer: b
Question (general): if rs . 510 be divided among a , b , c in such a way that a gets 2 / 3 of what b gets and b gets 1 / 4 of what c gets , then their shares are respectively ?
Options: a ) rs . 300 , b ) rs . 360 , c ) rs . 389 , d ) rs . 368 , e ) rs . 323
Rationale: "( a = 2 / 3 b and b = 1 / 4 c ) = a / b = 2 / 3 and b / c = 1 / 4 a : b = 2 : 3 and b : c = 1 : 4 = 3 : 12 a : b : c = 2 : 3 : 12 a ; s share = 510 * 2 / 17 = rs . 60 b ' s share = 510 * 3 / 17 = rs . 90 c ' s share = 510 * 12 / 17 = rs . 360 . answer : b"
Answer: b
Question (general): if p # q denotes the least common multiple of p and q , then p = ( ( 12 # 16 ) # ( 18 # 24 ) ) = ?
Options: a ) 216 , b ) 180 , c ) 144 , d ) 108 , e ) 72
Rationale: "there are several ways to find the least common multiple of two numbers . in this case , the most efficient method is to use the greatest common factor : ( a * b ) / ( gcf ab ) = lcm ab the greatest common factor of 12 and 16 is 4 . so , 12 # 16 = 12 * 16 / 4 = 48 . the greatest common factor of 18 and 24 is 6 . so , 18 # 24 = 18 * 24 / 6 = 72 finally , the greatest common factor of 48 and 72 is 24 . so , p = ( ( 12 # 16 ) # ( 18 # 24 ) ) = 48 # 72 = ( 48 * 72 ) / 24 = 2 * 72 = 144 the correct answer is c ."
Answer: c
Question (general): if ( 18 ^ a ) * 9 ^ ( 3 a – 1 ) = ( 2 ^ 6 ) ( 3 ^ b ) and a and b are positive integers , what is the value of a ?
Options: a ) 22 , b ) 11 , c ) 9 , d ) 6 , e ) 3
Rationale: "( 18 ^ a ) * 9 ^ ( 3 a – 1 ) = ( 2 ^ 6 ) ( 3 ^ b ) = 2 ^ a . 9 ^ a . 9 ^ ( 3 a – 1 ) = ( 2 ^ 6 ) ( 3 ^ b ) just compare powers of 2 from both sides answer = 6 = d"
Answer: d
Question (general): there are 8 teams in a certain league and each team plays each of the other teams exactly twice . if each game is played by 2 teams , what is the total number of games played ?
Options: a ) 15 , b ) 16 , c ) 28 , d ) 56 , e ) 64
Rationale: "every team plays with 7 teams . . . so total no of matches = 8 x 7 = 56 . now , each match is played twice = > 56 x 2 but 2 teams play a match = > 56 x 2 / 2 = 56 . ans : d"
Answer: d
Question (gain): a shopkeeper buys mangoes at the rate of 4 a rupee and sells them at 3.5 a rupee . find his net profit or loss percent ?
Options: a ) 13.2 % , b ) 15.2 % , c ) 14.28 % , d ) 32 1 / 3 % , e ) 33 1 / 2 %
Rationale: "the total number of mangoes bought by the shopkeeper be 12 . if he buys 4 a rupee , his cp = 3.5 he selling at 3.5 a rupee , his sp = 4 profit = sp - cp = 4 - 3.5 = 0.5 profit percent = 0.5 / 3.5 * 100 = 14.28 % answer : c"
Answer: c
Question (other): solution a is made up of alcohol and water mixed in the ratio of 21 : 4 by volume ; solution b is made up of alcohol and water mixed in the ratio of 2 : 3 by volume . if solution a and solution b are mixed in the ratio of 5 : 6 by volume , what percent of the resultant mixture is alcohol ?
Options: a ) 32.5 % , b ) 40 % , c ) 60 % , d ) 65 % , e ) can not be determined
Rationale: let mixture after mixing a and b is 110 ml ( number assumed for calculation because of 5 : 6 ) now solution a is 50 ml and solu b is 60 ml further in a 100 ml a contains 84 ml alch so 50 ml contain 42 ml in mix b 100 ml solution contain 40 ml alc , 60 ml of b , it will be 24 ml alcohol . so 42 + 24 = 66 in 110 ml solution which is 60 % answer : c
Answer: c
Question (general): at veridux corporation , there are 180 employees . of these , 90 are female , and the rest are males . there are a total of 40 managers , and the rest of the employees are associates . if there are a total of 135 male associates , how many female managers are there ?
Options: a ) 95 , b ) 20 , c ) 85 , d ) 75 , e ) 35
Rationale: "well , first let â € ™ s take care of the â € œ totals â €  . the numbers in the â € œ totals â €  row must add up . if 90 are females , the other 180 â € “ 90 = 90 must be males . similarly , the numbers in the â € œ totals â €  column must add up . if 40 are managers , then the other 180 â € “ 40 = 140 must be associates . now , in the â € œ associate â €  row , 135 + e = 140 , which means e = 5 â € ” the other 5 associates must be female . now , to find b , which is what the question is asking , we need only look at the sum in the â € œ female â €  column : b + 5 = 90 , which means b = 85 . there are fifteen female managers in this company . thus , the answer = ( c ) ."
Answer: c
Question (general): keats library purchases a number of new books , all in the category of biography , and the library does not acquire any other books . with the addition of the new biographies , the biography collection of the library amounts to 55 % of the total number of books in the library . if prior to the purchase , only 20 % of the books in keats library were biographies , by what percent has the number of biographies in the library increased ?
Options: a ) 270 % , b ) 310 % , c ) 350 % , d ) 390 % , e ) 430 %
Rationale: "let x be the number of new biographies added to the library . let b be the original number of biographies , so the original number of books was 5 b . 0.55 ( 5 b + x ) = b + x 1.75 b = 0.45 x x = 3.9 b the answer is d ."
Answer: d
Question (gain): after decreasing 24 % in the price of an article costs rs . 836 . find the actual cost of an article ?
Options: a ) 1667 , b ) 6789 , c ) 1200 , d ) 1100 , e ) 1421
Rationale: cp * ( 76 / 100 ) = 836 cp = 11 * 100 = > cp = 1100 answer : d
Answer: d
Question (geometry): two isosceles triangles have equal vertical angles and their areas are in the ratio 16 : 36 . find the ratio of their corresponding heights .
Options: a ) 4 / 6 , b ) 5 / 4 , c ) 3 / 2 , d ) 5 / 7 , e ) 2 / 3
Rationale: "we are basically given that the triangles are similar . in two similar triangles , the ratio of their areas is the square of the ratio of their sides and also , the square of the ratio of their corresponding heights . therefore , area / area = height ^ 2 / height ^ 2 = 16 / 36 - - > height / height = 4 / 6 . answer : a ."
Answer: a
Question (general): in a weight - lifting competition , the total weight of joe ' s two lifts was 1500 pounds . if twice the weight of his first lift was 300 pounds more than the weight of his second lift , what was the weight , in pounds , of his first lift ?
Options: a ) 225 , b ) 275 , c ) 325 , d ) 350 , e ) 600
Rationale: "this problem is a general word translation . we first define variables and then set up equations . we can define the following variables : f = the weight of the first lift s = the weight of the second lift we are given that the total weight of joe ' s two lifts was 1500 pounds . we sum the two variables to obtain : f + s = 1500 we are also given that twice the weight of his first lift was 300 pounds more than the weight of his second lift . we express this as : 2 f = 300 + s 2 f – 300 = s we can now plug in ( 2 f – 300 ) for s into the first equation , so we have : f + 2 f – 300 = 1500 3 f = 1,800 f = 600 answer is e ."
Answer: e
Question (general): the cash realised on selling a 14 % stock is rs . 109.25 , brokerage being 1 / 4 % is
Options: a ) 123 , b ) 109 , c ) 100 , d ) 156 , e ) 240
Rationale: "explanation : cash realised = rs . ( 109.25 - 0.25 ) = rs . 109 . answer : b"
Answer: b
Question (other): if 47.5 % of the 880 students at a certain college are enrolled in biology classes , how many students at the college are not enrolled in a biology class ?
Options: a ) 110 , b ) 330 , c ) 550 , d ) 462 , e ) 880
Rationale: "students enrolled in biology are 47.5 % and therefore not enrolled are 52.5 % . so of 880 is 880 * . 525 = 462 answer is d 462"
Answer: d
Question (physics): two ships are sailing in the sea on the two sides of a lighthouse . the angle of elevation of the top of the lighthouse is observed from the ships are 30 ° and 45 ° respectively . if the lighthouse is 100 m high , the distance between the two ships is :
Options: a ) 173 m , b ) 200 m , c ) 273 m , d ) 300 m , e ) 373 m
Rationale: let ab be the lighthouse and c and d be the positions of the ships . then , ab = 100 m , acb = 30 ° and adb = 45 ° . ab = tan 30 ° = 1 ac = ab x 3 = 1003 m . ac 3 ab = tan 45 ° = 1 ad = ab = 100 m . ad cd = ( ac + ad ) = ( 1003 + 100 ) m = 100 ( 3 + 1 ) = ( 100 x 2.73 ) m = 273 m . answer = c
Answer: c
Question (physics): a tank can supply water to a village for 80 days . if a leak at the bottom of the tank drains out 10 liters per day , the supply lasts for 60 days only . for how many days will the supply last if the leak drains out 20 liters per day ?
Options: a ) 42 , b ) 45 , c ) 48 , d ) 50 , e ) 55
Rationale: "losing 10 liters per day results in a loss of 600 liters in 60 days . so , those 600 liters were for 20 days , making daily consumption of the village 30 liters per day . thus the capacity of the tank is 30 * 80 = 2400 liters . losing 20 liters plus 30 liters gives 50 liters per day . at this rate the supply will last 2400 / 50 = 48 days . the answer is c ."
Answer: c
Question (physics): a can do a work in 25 days and b can do it in 10 days . in how many days a and b can do the work ?
Options: a ) 20 days , b ) 10 days , c ) 6 8 / 7 days , d ) 8 days , e ) 7 days
Rationale: "explanation : a ' s 1 day ' s work = 1 / 25 b ' s 1 day ' s work = 1 / 10 they work together = 1 / 25 + 1 / 10 = 7 / 50 = 50 / 7 = 6 8 / 7 days answer : option c"
Answer: c
Question (general): a ' and ' b ' are positive integers such that their lcm is 20 and their hcf is 1 . what is the difference between the maximum and minimum possible values of ' a - b ' ?
Options: a ) 28 , b ) 29 , c ) 34 , d ) 38 , e ) 36
Rationale: possible values of a and b can be 54 ; 45 and 120 ; 201 maximum possible value for a - b is 20 - 1 = 19 minimum possible value for a - b is 1 - 20 = - 19 19 - ( - 19 ) = 38 ans is d
Answer: d
Question (geometry): the size of a television screen is given as the length of the screen ' s diagonal . if the screens were flat , then the area of a square 18 - inch screen would be how many square inches greater than the area of a square 16 - inch screen ?
Options: a ) 2
b ) 4
c ) 34
d ) 38
e ) 40
Rationale: pythogoras will help here ! let the sides be x and diagonal be d then d ^ 2 = 2 x ^ 2 and area = x ^ 2 now plug in the given diagonal values to find x values and then subtract the areas ans will be 18 ^ 2 / 2 - 16 ^ 2 / 2 = 68 / 2 = 34 ans c .
Answer: c
Question (gain): an alloy weighing 24 ounces is 70 percent gold . how many ounces of pure gold must be added to create an alloy that is 80 percent gold ?
Options: a ) 6 , b ) 9 , c ) 12 , d ) 24 , e ) 48
Rationale: "in 24 ounces , gold is 24 * ( 70 / 100 ) = 16.8 ounces . now we add x ounces of pure gold to make it 90 % gold . so 16.8 + x = ( 24 + x ) * 80 / 100 = > x = 12 . answer is c ."
Answer: c
Question (general): find the principle on a certain sum of money at 5 % per annum for 2 2 / 5 years if the amount being rs . 1456 ?
Options: a ) 1000 , b ) 2217 , c ) 2889 , d ) 2777 , e ) 1300
Rationale: "1456 = p [ 1 + ( 5 * 12 / 5 ) / 100 ] p = 1300 answer : e"
Answer: e
Question (general): what is the 4 digit no . in which the 1 st digit is 1 / 3 of the second , the 3 rd is the sum of the 1 st and 2 nd , and the last is 3 times the second ?
Options: a ) 1123 , b ) 1234 , c ) 1349 , d ) 1455 , e ) 1567
Rationale: first digit is 1 / 3 second digit = > the numbers can be 1 & 3 , 2 & 6 , 3 & 9 . first + second = third = > we can eliminate 3 & 9 since 3 + 9 = 12 . last is 3 times the second = > we can eliminate option 2 & 6 since 3 * 6 = 18 . hence the number is 1349 c
Answer: c
Question (general): what number is 76 more than one - fourth of itself ?
Options: a ) 101 , b ) 225 , c ) 304 , d ) 324 , e ) 336
Rationale: "1 / 4 x + 76 = x that means 76 = 3 / 4 x x = ( 76 * 4 ) / 3 = 304 / 3 = 101 a is the answer"
Answer: a
Question (general): a certain shade of gray paint is obtained by mixing 3 parts of white paint with 5 parts of black paint . if 2 gallons of the mixture is needed and the individual colors can be purchased only in one gallon or half gallon cans , what is the least amount of paint w , in gallons , that must be purchased in order to measure out the portions needed for the mixture ?
Options: a ) 2 , b ) 2 1 / 2 , c ) 3 , d ) 3 1 / 2 , e ) 4
Rationale: "given w : b = 3 : 5 that means say 3 gallons of white paint + 5 gallons of black paint = 8 gallons of paint mixture . but we want least amount of whiteblack paints for minimum of 2 gallons of mixture , so lets reduce keeping same ratio , 1.5 : 2.5 gives 1.5 + 2.5 = 4 gallons of mixture , but we want only 2 gallons , lets further reduce 0.75 : 1.25 gives 1 + 1.5 = 2.5 gallons of mixture . this looks ok , but lets reduce further just to be sure 0.375 : 0.625 gives 0.5 + 1 = 1.5 gallons of mixture , thats less than 2 gallons of mixture , so not acceptable . so correct ans is 2.5 gallons . b"
Answer: b
Question (physics): someone on a skateboard is traveling 15 miles per hour . how many feet does she travel in 30 seconds ? ( 1 mile = 5280 feet )
Options: a ) 600 ft , b ) 660 ft , c ) 670 ft , d ) 680 ft , e ) 700 ft
Rationale: "per second = > 15 * 5280 ft / 60 * 60 = 22 ft 30 seconds = > 22 * 30 = 660 ft answer : b"
Answer: b
Question (physics): a company produces 72000 bottles of water everyday . if a case can hold 10 bottles of water . how many cases are required by the company to hold its one day production
Options: a ) 2000 , b ) 4500 , c ) 5000 , d ) 7200 , e ) 9000
Rationale: "number of bottles that can be held in a case = 10 number of cases required to hold 72000 bottles = 72000 / 10 = 7200 cases . so the answer is d = 7200"
Answer: d
Question (physics): the sum of 99 consecutive integers is 9999 . what is the greatest integer in the set ?
Options: a ) 100 , b ) 120 , c ) 149 , d ) 150 , e ) 151
Rationale: "sum of n numbers = ( n ( 2 a + ( n - 1 ) d ) ) / 2 where n = no of terms a = 1 st term , d - difference between two terms ( ie d = a 2 - a 1 ) here sum = 9999 , n = 99 d = 1 ( since consecutive numbers ) 9999 = ( 99 / 2 ) * ( 2 a + ( 99 - 1 ) 1 ) from this ' a ' ( ie the 1 st term ) = 52 nth term in a sequence : nth term = a + ( n - 1 ) d here a = 52 , n = 99 , d = 1 so nth term = 52 + ( 99 - 1 ) * 1 therefore nth term = 150 answer : d"
Answer: d
Question (physics): a train of 24 carriages , each of 60 meters length , when an engine also of 60 meters length is running at a speed of 60 kmph . in what time will the train cross a bridge 3.5 km long ?
Options: a ) 4 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: "d = 25 * 60 + 3500 = 5000 m t = 5000 / 60 * 18 / 5 = 300 sec = 5 mins answer : c"
Answer: c
Question (general): the tax on a commodity is diminished by 20 % and its consumption increased by 15 % . the effect on revenue is ?
Options: a ) 9 % decrease , b ) 8 % decrease , c ) 6 % decrease , d ) 1 % decrease , e ) 2 % decrease
Rationale: "100 * 100 = 10000 80 * 115 = 9200 - - - - - - - - - - - 10000 - - - - - - - - - - - 800 100 - - - - - - - - - - - ? = > 8 % decrease answer : b"
Answer: b
Question (gain): the length of a rectangular floor is more than its breadth by 200 % . if rs . 484 is required to paint the floor at the rate of rs . 3 / sq m , what would be the length of the floor ?
Options: a ) 12 , b ) 18 , c ) 20 , d ) 22 , e ) 24
Rationale: "let the length and the breadth of the floor be l m and b m respectively . l = b + 200 % of b = l + 2 b = 3 b area of the floor = 484 / 3 = 161.33 sq m l b = 161.33 i . e . , l * l / 3 = 161.33 l ^ 2 = 484 = > l = 22 . d"
Answer: d
Question (physics): a train running at the speed of 50 km / hr crosses a pole in 9 seconds . find the length of the train ?
Options: a ) 125 , b ) 272 , c ) 278 , d ) 277 , e ) 112
Rationale: "speed = 50 * ( 5 / 18 ) m / sec = 125 / 9 m / sec length of train ( distance ) = speed * time ( 125 / 9 ) * 9 = 125 meter answer : a"
Answer: a
Question (general): the expression x # y denotes the product of the consecutive multiples of 3 between x and y , inclusive . what is the sum of the exponents in the prime factorization of 21 # 33 ?
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: "first , let ' s translate the expression 21 # 33 , using the definition given : 21 # 33 = 21 × 24 × 27 × 30 × 33 we need the prime factorization of this product . let ' s factor out 3 from each multiple . 21 # 33 = 3 ^ 6 ( 7 × 8 × 9 × 10 × 11 ) now let ' s replace each consecutive integer with its prime factorization : 21 # 33 = 3 ^ 5 ( 7 × 2 ^ 3 × 3 ^ 2 × ( 2 × 5 ) × 11 ) let ' s group the prime bases : 21 # 33 = 2 ^ 4 × 3 ^ 7 × 5 × 7 × 11 the sum of the exponents is 4 + 7 + 1 + 1 + 1 = 14 the answer is c ."
Answer: c
Question (gain): after decreasing 20 % in the price of an article costs rs . 620 . find the actual cost of an article ?
Options: a ) 775 , b ) 620 , c ) 750 , d ) 800 , e ) 720
Rationale: "cp * ( 80 / 100 ) = 620 cp = 7.75 * 100 = > cp = 775 answer : a"
Answer: a
Question (general): 90 % of the population of a village is 23040 . the total population of the village is ?
Options: a ) 32256 , b ) 24000 , c ) 24936 , d ) 25600 , e ) none
Rationale: "answer ∵ 90 % of p = 23040 ∴ p = ( 23040 x 100 ) / 90 = 25600 correct option : d"
Answer: d
Question (geometry): if y is the smallest positive integer such that 8,820 multiplied by y is the square of an integer , then y must be
Options: a ) 2 , b ) 5 , c ) 6 , d ) 7 , e ) 14
Rationale: "i just tried plugging in the numbers and found out that 5 * 8820 = 44 , 100 , which is a square of 210 b"
Answer: b
Question (physics): a train 100 m long crosses a platform 125 m long in 40 sec ; find the speed of the train ?
Options: a ) 36.21 , b ) 77.11 , c ) 54.12 , d ) 33.0 , e ) 20.25
Rationale: "d = 100 + 125 = 225 t = 40 s = 225 / 40 * 18 / 5 = 20.25 kmph answer : e"
Answer: e
Question (physics): a group of men decided to do a work in 15 days , but 8 of them became absent . if the rest of the group did the work in 18 days , find the original number of men ?
Options: a ) 15 , b ) 48 , c ) 54 , d ) 33 , e ) 45
Rationale: "original number of men = 8 * 18 / ( 18 - 15 ) = 48 answer is b"
Answer: b
Question (probability): x , y , and z are all unique numbers . if x is chosen randomly from the set { 5 , 6 , 7 , 8 , 9 , 10 , 11 } and y and z are chosen randomly from the set { 20 , 21 , 22 , 23 } , what is the probability that x and y are prime and z is not ?
Options: a ) 1 / 5 , b ) 3 / 20 , c ) 1 / 7 , d ) 2 / 15 , e ) 3 / 28
Rationale: "p ( x is prime ) = 3 / 7 p ( y is prime ) = 1 / 4 if y is prime , then z is not prime since y and z are unique . then the probability is 3 / 7 * 1 / 4 = 3 / 28 the answer is e ."
Answer: e