Cheukting/mathqa huggingface dataset:
Question (physics): a can run 4 times as fast as b and gives b a start of 75 m . how long should the race course be so that a and b might reach in the same time ?
Options: a ) 70 m , b ) 60 m , c ) 100 m , d ) 65 m , e ) 75 m
Rationale: "speed of a : speed of b = 4 : 1 means in a race of 4 m a gains 3 m . then in a race of 75 m he gains 75 * ( 4 / 3 ) i . e 100 m answer : c"
Answer: c
Question (gain): when the price of an article was reduced by 15 % its sale increased by 80 % . what was the net effect on the sale ?
Options: a ) 44 % increase , b ) 44 % decrease , c ) 53 % increase , d ) 66 % increase , e ) 66 % decrease
Rationale: if n items are sold for $ p each , revenue is $ np . if we reduce the price by 15 % , the new price is 0.85 p . if we increase the number sold by 80 % , the new number sold is 1.8 n . so the new revenue is ( 0.85 p ) ( 1.8 n ) = 1.53 np , which is 1.53 times the old revenue , so is 53 % greater . answer : c
Answer: c
Question (general): a certain characteristic in a large population has a distribution that is symmetric about the mean m . if 64 percent of the distribution lies within one standard deviation d of the mean , what percent of the distribution is less than m + d ?
Options: a ) 16 % , b ) 32 % , c ) 48 % , d ) 82 % , e ) 92 %
Rationale: "this is easiest to solve with a bell - curve histogram . m here is equal to µ in the gaussian normal distribution and thus m = 50 % of the total population . so , if 64 % is one st . dev , then on either side of m we have 64 / 2 = 32 % . so , 32 % are to the right and left of m ( = 50 % ) . in other words , our value m + d = 50 + 32 = 82 % goingfrom the mean m , to the right of the distributionin the bell shaped histogram . . this means that 82 % of the values are below m + d . like i said , doing it on a bell - curve histogram is much easier to fullygethow this works , or you could apply gmat percentile jargon / theory to it d"
Answer: d
Question (general): two trains of equal are running on parallel lines in the same direction at 46 km / hr and 36 km / hr . the faster train passes the slower train in 27 sec . the length of each train is ?
Options: a ) 50 , b ) 37.5 , c ) 27 , d ) 28 , e ) 21
Rationale: let the length of each train be x m . then , distance covered = 2 x m . relative speed = 46 - 36 = 10 km / hr . = 10 * 5 / 18 = 25 / 9 m / sec . 2 x / 27 = 25 / 9 = > x = 37.5 . answer : b
Answer: b
Question (general): sam ’ s car was fined when he gave joe and peter a ride , so they decided to help sam pay the fine . joe paid $ 7 more than 1 / 4 of the fine and peter paid $ 7 less than 1 / 3 of the fine , leaving pay $ 12 less than 1 / 2 the fine to complete the payment . what fraction of the fine did sam pay ?
Options: a ) $ 65 , b ) $ 55 , c ) $ 50 , d ) $ 60 , e ) $ 45
Rationale: call the fine f . joe paid ( 1 / 4 ) f + 4 and peter paid ( 1 / 3 ) f – 4 , leaving ( 1 / 2 ) f – 5 left . if we add those three up , they should add up to f . f = [ ( 1 / 4 ) f + 7 ] + [ ( 1 / 3 ) f – 7 ] + [ ( 1 / 2 ) f – 12 ] f = ( 1 / 4 ) f + ( 1 / 3 ) f + ( 1 / 2 ) f – 12 multiply all terms by 12 to clear the fractions . 12 f = 3 f + 4 f + 6 f – 144 12 f = 13 f – 144 – f = – 144 f = 144 well , if the fine cost $ 144 , then sam paid the part not covered by joe or peter . half the fine is $ 72 , and sam paid $ 12 less than this : $ 60 . answer = d
Answer: d
Question (physics): if two projectiles are launched at the same moment from 1998 km apart and travel directly towards each other at 444 km per hour and 555 km per hour respectively , how many minutes will it take for them to meet ?
Options: a ) 90 , b ) 100 , c ) 110 , d ) 120 , e ) 130
Rationale: "the projectiles travel a total of 999 km per hour . the time to meet is 1998 / 999 = 2 hours = 120 minutes the answer is d ."
Answer: d
Question (general): after spending rs . 5000 on rent , rs . 1500 on milk , rs . 4500 on groceries , rs . 2500 on childrens education rs . 2000 on petrol and rs . 5650 on miscellaneous expenses , mr . kishore saved 10 % of his monthly salary . how much did he save in rs . ?
Options: a ) 2160 , b ) 2350 , c ) 2000 , d ) 2300 , e ) none of these
Rationale: explanation : total exp = 5000 + 1500 + 4500 + 2500 + 2000 + 5650 = 21150 exp in % = 100 - 10 = 90 % , 21150 = 90 % saving = 10 % = 21150 x 10 / 90 = rs . 2350 answer : b
Answer: b
Question (general): a large box contains 15 small boxes and each small box contains 25 chocolate bars . how many chocolate bars are in the large box ?
Options: a ) a ) 220 , b ) b ) 490 , c ) c ) 375 , d ) d ) 450 , e ) e ) 690
Rationale: "the only thing you have to do is a simple multiply we have : 15 * 25 = 375 correct answer is : c ) 375"
Answer: c
Question (general): an assembly line produces 90 cogs per hour until an initial order of 60 cogs is completed . the speed of the assembly line is then immediately decreased so that it only produces 60 cogs per hour until another 60 cogs are produced . what is the overall average output , in cogs per hour , for the assembly line during this whole time ?
Options: a ) 68 , b ) 69 , c ) 70 , d ) 71 , e ) 72
Rationale: "the time to produce the first 60 cogs is 60 / 90 = 2 / 3 hours . the time to produce the next 60 cogs is 60 / 60 = 1 hour . the average output is 120 cogs / ( 5 / 3 ) hours = 72 cogs per hour . the answer is e ."
Answer: e
Question (general): there has been successive increases of 25 % and then 15 % in the price of gas from the previous month . by what percentage should a driver reduce gas consumption so that the expenditure does not change ?
Options: a ) 30 % , b ) 50 % , c ) 66.66 % , d ) 15 % , e ) 75 %
Rationale: let p be the original price per unit of gas . let x be the original gas consumption . let y be the reduced gas consumption . y * 1.15 * 1.25 * p = x * p y = x / ( 1.15 * 1.25 ) which is about 0.7 x which is a decrease of about 30 % . the answer is a .
Answer: a
Question (physics): a train covers a distance of 12 km in 5 min . if it takes 6 sec to pass a telegraph post , then the length of the train is ?
Options: a ) 120 m , b ) 180 m , c ) 240 m , d ) 220 m , e ) 280 m
Rationale: "speed = ( 12 / 5 * 60 ) km / hr = ( 144 * 5 / 18 ) m / sec = 40 m / sec . length of the train = 40 * 6 = 240 m . answer : c"
Answer: c
Question (general): ab + ba ___ 202 in the addition problem above , a and b represent digits in two different two - digit numbers . what is the sum of a and b ?
Options: a ) 6 , b ) 8 , c ) 9 , d ) 20 , e ) 14
Rationale: two ways to do it . . 1 ) straight logic . . only 20 fits in . . d
Answer: d
Question (physics): an industrial loom weaves 0.128 metres of cloth every second . approximately , how many seconds will it take for the loom to weave 29 metre of cloth ?
Options: a ) 175 seconds , b ) 195 seconds , c ) 155 seconds , d ) 227 seconds , e ) 115 seconds
Rationale: "explanation : let the time required by x seconds . then , more cloth means more time ( direct proportion ) so , 0.128 : 1 : : 29 : x = > x = { \ color { blue } \ frac { 29 \ times 1 } { 0.128 } } = > x = 226.56 so time will be approx 227 seconds answer : d"
Answer: d
Question (physics): the sum of three consecutive even numbers is 36 , find the first number ?
Options: a ) 21 , b ) 18 , c ) 12 , d ) 16 , e ) 10
Rationale: "let the first number be n let the second number be n + 2 let the third number be n + 4 n + n + 2 + n + 4 = 36 combine like terms : 3 n + 6 = 36 3 n = 36 - 6 3 n = 30 3 n = 30 n = 10 n + 2 = 12 n + 4 = 16 the first number is 10 answer : e"
Answer: e
Question (general): 30 liters of a mixture is created by mixing liquid p and liquid q in the ratio 3 : 2 . how many liters of liquid q must be added to make the ratio 3 : 4 ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: "let x be the amount of liquid q to be added . ( 2 / 5 ) * 30 + x = ( 4 / 7 ) * ( 30 + x ) 420 + 35 x = 600 + 20 x 15 x = 180 x = 12 the answer is c ."
Answer: c
Question (general): . for the fifa world cup , paul the octopus has been predicting the winner of each match with amazing success . it is rumored that in a match between 2 teams a and b , paul picks a with the same probability as a ’ s chances of winning . let ’ s assume such rumors to be true and that in a match between ghana and bolivia ; ghana the stronger team has a probability of 2 / 3 of winning the game . what is the probability that paul will correctly pick the winner of the ghana - bolivia game ?
Options: a ) 59 , b ) 88 , c ) 77 , d ) 26 , e ) 18
Rationale: the probability that paul correctly picks the winner = ( a ' s chances of winning ) x ( pauls picking the winner corectly ) + ( a ' s chances of loosing ) x ( paul picks wrongly ) = 23 × 23 + 13 × 13 = 59 answer : a
Answer: a
Question (general): john has 10 pairs of matched socks . if he loses 5 individual socks , what is the greatest number of pairs of matched socks he can have left ?
Options: a ) 8 , b ) 7 , c ) 5 , d ) 4 , e ) 3
Rationale: because we have to maximize the pair of matched socks , we will remove 2 pairs ( 4 socks ) out of 10 pairs 1 sock from the 3 th pair . thus the no of matching socks pair remaining = 10 - 3 = 7 answer b
Answer: b
Question (general): if { x } is the product of all even integers from 1 to x inclusive , what is the greatest prime factor of { 18 } + { 16 } ?
Options: a ) 23 , b ) 20 , c ) 11 , d ) 19 , e ) 2
Rationale: soln : { 18 } + { 16 } = 18 * { 16 } + { 16 } = 19 * { 16 } answer : d
Answer: d
Question (general): a rainstorm increased the amount of water stored in state j reservoirs from 125 billion gallons to 150 billion gallons . if the storm increased the amount of water in the reservoirs to 80 percent of total capacity , approximately how many billion gallons of water were the reservoirs short of total capacity prior to the storm ?
Options: a ) 9 , b ) 14 , c ) 25 , d ) 30 , e ) 44
Rationale: after the reservoir is filled to 150 gallons the amount of water is at 80 % - which means that 20 % of the reservoir is empty . to figure out what that 20 % is approximate : 150 gallons / 80 percent = x gallons / 20 percent , therefore , x = 37.5 gallons , answer choices a , b , c , d are below 37.5 . we know that the reservoir must be short more than 37.5 gallons , therefore , the only possible choice is e .
Answer: e
Question (general): in the graduating class of a certain college , 48 percent of the students are male and 52 percent are female . in this class 40 percent of the male and 50 percent of the female students are 25 years old or older . if one student in the class is randomly selected , approximately what is the probability that he or she will be less than 25 years old ?
Options: a ) a ) 0.9 , b ) b ) 0.5 , c ) c ) 0.45 , d ) d ) 0.3 , e ) e ) 0.25
Rationale: "percent of students who are 25 years old or older is 0.4 * 48 + 0.5 * 52 = ~ 45 , so percent of people who are less than 25 years old is 100 - 45 = 55 . answer : b ."
Answer: b
Question (general): if ( a – b ) is 7 more than ( c + d ) and ( a + b ) is 3 less than ( c – d ) , then ( a – c ) is :
Options: a ) 6 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "( a – b ) – ( c + d ) = 7 and ( c – d ) – ( a + b ) = 3 = > ( a – c ) – ( b + d ) = 7 and ( c – a ) – ( b + d ) = 3 = > ( b + d ) = ( a – c ) – 7 and ( b + d ) = ( c – a ) – 3 = > ( a – c ) – 7 = ( c – a ) – 3 = > 2 ( a – c ) = 4 = > ( a – c ) = 2 answer : b"
Answer: b
Question (geometry): a person jogged 10 times along the perimeter of a rectangular field at the rate of 12 kilometers per hour for 30 minutes . if field has a length that is twice its width , find the area of the field in square meters .
Options: a ) 20,000 square meters
b ) 10,000 square meters
c ) 30,000 square meters
d ) 40,000 square meters
e ) 50,000 square meters
Rationale: let us first find the distance d jogged distance = rate * time = ( 12 km / hr ) * 30 minutes = ( 12 km / hr ) * 0.5 hr = 6 km the distance of 6 km corresponds to 10 perimeters and therefore 1 perimeter is equal to 6 km / 10 = 0.6 km = 0.6 * 1000 meters = 600 meters let l and w be the length and width of the field . the length is twice the width . hence l = 2 w the perimeter is 600 meters and is given by 2 ( l + w ) = 600 substitute l by 2 w 2 ( 2 w + w ) = 600 simplify and solve for w 4 w + 2 w = 600 6 w = 600 w = 100 find l l = 2 w = 200 find the area a of the rectangle a = l * w = 200 * 100 = 20,000 square meters correct answer a
Answer: a
Question (general): a man is 27 years older than his son . in two years , his age will be twice the age of his son . the present age of the son is ?
Options: a ) 11 , b ) 25 , c ) 27 , d ) 22 , e ) 91
Rationale: let the son ' s present age be x years . then , man ' s present age = ( x + 27 ) years . ( x + 27 ) + 2 = 2 ( x + 2 ) x + 29 = 2 x + 4 = > x = 25 . answer : b
Answer: b
Question (other): john distributes his pencil among his 4 friends rose , mary , ranjan , and rohit in the ratio 1 / 2 : 1 / 3 : 1 / 4 : 1 / 5 . what is the minimum no . of pencils that the person should have ?
Options: a ) 65 , b ) 68 , c ) 70 , d ) 77 , e ) 80
Rationale: "rakesh : rahul : ranjan : rohit = 1 / 2 : 1 / 3 : 1 / 4 : 1 / 5 step 1 : at first we need to do is lcm of 2 , 3,4 and 5 is 60 . step 2 : then pencil are distributed in ratio among friends , rakesh = ( 1 / 2 x 60 ) = 30 . rahul = ( 1 / 3 x 60 ) = 20 . ranjan = ( 1 / 4 x 60 ) = 15 . rohit = ( 1 / 5 x 60 ) = 12 . step 3 : total number of pencils are ( 30 x + 20 x + 15 x + 12 x ) = 77 x . for minimum number of pencils x = 1 . the person should have atleast 77 pencils . d )"
Answer: d
Question (gain): a particular library has 75 books in a special collection , all of which were in the library at the beginning of the month . these book are occasionally loaned out through an inter - library program . if , by the end of the month , 70 percent of books that were loaned out are returned and there are 63 books in the special collection at that time , how many books of the special collection were loaned out during that month ?
Options: a ) 20 , b ) 30 , c ) 35 , d ) 40 , e ) 55
Rationale: "i did n ' t understand how did we get 100 ? total = 75 books . 65 % of books that were loaned out are returned - - > 100 % - 70 % = 30 % of books that were loaned out are not returned . now , there are 63 books , thus 76 - 63 = 12 books are not returned . { loaned out } * 0.30 = 7 - - > { loaned out } = 40 . answer : d ."
Answer: d
Question (geometry): all the faces of cubes are painted with red colour . it is then cut into 64 equal small cubes . find how many small cubes have no faces coloured ?
Options: a ) 24 , b ) 8 , c ) 16 , d ) 0 , e ) 4
Rationale: "there are 64 small cubes , hence one side side of the big cube is 3 √ 64 = 4 cm number of small cubes having only one faces coloured = ( x - 2 ) ^ 3 here , x = side of big cube / side of small cube x = 4 / 1 x = 4 required number = ( 4 - 2 ) ^ 3 = 8 answer : b"
Answer: b
Question (general): [ ( 3.242 x 16 ) / 100 ] = ?
Options: a ) 0.045388 , b ) 4.5388 , c ) 0.051872 , d ) 473.88 , e ) none of these
Rationale: "answer multiplying 3.242 x 16 = 5.1872 now divide 5.1872 by 100 so , 5.1872 ÷ 100 = 0.051872 ∴ shift the decimal two places to the left as 100 correct option : c"
Answer: c
Question (general): sabrina is contemplating a job switch . she is thinking of leaving her job paying $ 90000 per year to accept a sales job paying $ 45000 per year plus 15 percent commission for each sale made . if each of her sales is for $ 1500 , what is the least number of sales she must make per year if she is not to lose money because of the job change ?
Options: a ) 57 , b ) 177 , c ) 178 , d ) 377 , e ) 200
Rationale: lets say she sales x items so her commission will be : x * 1500 * 15 / 100 = 225 x salary difference is : 90000 - 45000 = 45000 so commission must at least be equal to salary difference i . e . x = 45000 / 225 = 200 ( approx ) . hence answer is e
Answer: e
Question (general): if ( 1 – 1.25 ) n = 2 , then n =
Options: a ) − 400 , b ) − 140 , c ) − 8 , d ) 4 , e ) 400
Rationale: "( 1 – 1.25 ) n = 2 simplify to get : - 0.25 n = 2 rewrite as ( - 1 / 4 ) n = 2 multiply both sides by - 4 to get : n = - 8 answer : c"
Answer: c
Question (general): a computer manufacturer produces a certain electronic component at a cost of $ 80 per component . shipping costs for delivering the components are $ 6 per unit . further , the manufacturer has costs of $ 16,500 a month related to the electronic component regardless of how many it produces . if the manufacturer produces and sells 150 components a month , what is the lowest price it can sell them for such that the costs do n ' t exceed the revenues ?
Options: a ) $ 28 , b ) $ 82 , c ) $ 110 , d ) $ 138 , e ) $ 196
Rationale: "by the question , the equation would be 150 p - 86 * 150 - 16500 = 0 p being the price we want to find and equation resulting zero means revenue and costs are equal so we can get the minimum price of the component . solving the equation , we get p = $ 196 . answer e for me ."
Answer: e
Question (physics): an outlet pipe can empty 2 / 3 of a cistern in 16 minutes . in 8 minutes , what part of the cistern will be emptied ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 2 / 5 , e ) 3 / 10
Rationale: 8 / 16 * 2 / 3 = 1 / 3 the answer is b .
Answer: b
Question (general): if a ã — b = 2 a - 3 b + ab , then 3 ã — 4 + 4 ã — 3 is equal to :
Options: a ) 17 , b ) 23 , c ) 24 , d ) 25 , e ) 26
Rationale: "explanation : 3 ã — 4 + 4 ã — 3 = ( 2 ã — 3 - 3 ã — 4 + 3 ã — 4 ) + ( 2 ã — 4 - 3 ã — 3 + 4 ã — 3 ) = ( 6 + 8 - 9 + 12 ) = 17 . answer : a"
Answer: a
Question (general): the simple interest on a sum of money will be rs . 1000 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 ) 8981 , b ) 3799 , c ) 1200 , d ) 2693 , e ) 2000
Rationale: "p - - - 10 - - - - 1000 p - - - 5 - - - - - 500 3 p - - - 5 - - - - - 1500 - - - - - - = > 2000 answer : e"
Answer: e
Question (gain): the cash difference between the selling prices of an article at a profit of 4 % and 8 % is rs . 3 . the ratio of the two selling prices is ?
Options: a ) 52 : 56 , b ) 52 : 53 , c ) 52 : 54 , d ) 22 : 56 , e ) 52 : 51
Rationale: let c . p . of the article be rs . x . then , required ratio = 104 % of x / 108 % of x = 104 / 108 = 52 / 54 = 52 : 54 answer : c
Answer: c
Question (other): if shares of two persons in profits are rs . 700 and rs . 300 then ratio of their capitals is
Options: a ) 3 : 4 , b ) 2 : 3 , c ) 7 : 3 , d ) 1 : 3 , e ) 1 : 5
Rationale: "total profit = 1000 ratio = 700 / 300 = 7 : 3 answer : c"
Answer: c
Question (geometry): a rectangular room has the rectangular shaped rug shown as above figure such that the rug ’ s area is 160 square feet and its length is 6 feet longer than its width . if the uniform width between the rug and room is 6 feet , what is the area of the region uncovered by the rug ( shaded region ) , in square feet ?
Options: a ) 32 , b ) 456 , c ) 40 , d ) 46 , e ) 104
Rationale: "rug ' s area = 160 which is ( x ) x ( 6 + x ) = 160 so x = 10 rug maintains a uniform distance of 6 feet so room has dimension 10 + 12 and 16 + 12 i . e . 22 and 28 area of room 22 x 28 = 616 area covered is 160 so uncovered area is 616 - 160 = 456 ( answer b )"
Answer: b
Question (general): an advertising agency finds that , of its 180 clients , 115 use television , 110 use radio and 130 use magazines . also , 85 use television and magazines , 75 use television and radio , 95 use radio and magazines . how many use all the 3 ?
Options: a ) 56 , b ) 70 , c ) 90 , d ) 98 , e ) 80
Rationale: total = 180 television = 115 radio = 110 magazine = 130 all the three = 180 - 115 - 110 - 130 + 85 + 75 + 95 = 80 answer e
Answer: e
Question (general): 8 friends met for lunch at an expensive restaurant , and everyone decided to contribute equally to the total bill of $ 290 . if one of the friends had a coupon for 29 % off the total bill , and if each friend still contributed equally after the coupon was applied to the bill , how much did each friend pay ?
Options: a ) $ 90 , b ) $ 70 , c ) $ 45 , d ) $ 37 , e ) $ 25
Rationale: 290 * 0,29 = 84 290 - 84 = 206 206 / 8 = 25 answer e
Answer: e
Question (geometry): for a right angle triangle the hypotenuse is 5 and base is 3 . what is the area of the triangle ?
Options: a ) 6
b ) 7
c ) 8
d ) 9
e ) 10
Rationale: as we know that for a right angle triangle the are is 1 / 2 * base * height we know the base = 3 we need to calculate the height hypotenuse = h = 5 base = b = 3 height = c = ? as per pythagoras h ^ 2 = b ^ 2 + c ^ 2 5 ^ 2 = 3 ^ 2 + c ^ 2 25 = 9 + c ^ 2 c ^ 2 = 25 - 9 c ^ 2 = 16 c = 4 height = 4 area = 1 / 2 * base * height = 1 / 2 * 3 * 4 = 6 square units ans : a
Answer: a
Question (physics): during a car trip , maria stopped to rest after she traveled 1 / 2 of the total distance to her destination . she stopped again after she traveled 1 / 4 of the distance remaining between her first stop and her destination , and then she drove the remaining 210 miles to her detination . what was the total distance , in miles from maria ' s starting point to her destination ?
Options: a ) 280 , b ) 320 , c ) 360 , d ) 420 , e ) 560
Rationale: "easy 560 is the answer . 3 / 4 ( x / 2 ) = 210 x = 210 * 8 / 3 = 560 . answer e"
Answer: e
Question (physics): a train 1000 m long can cross an electric pole in 200 sec and then find the speed of the train ?
Options: a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20
Rationale: "length = speed * time speed = l / t s = 1000 / 200 s = 5 m / sec speed = 5 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 18 kmph answer : d"
Answer: d
Question (physics): joshua and jose work at an auto repair center with 6 other workers . for a survey on health care insurance , 2 of the 6 workers will be randomly chosen to be interviewed . what is the probability that joshua and jose will both be chosen ?
Options: a ) 1 / 15 , b ) 1 / 12 , c ) 1 / 28 , d ) 1 / 6 , e ) 1 / 3
Rationale: "two methods 1 ) probability of chosing josh first = 1 / 8 probability of chosing jose second = 1 / 7 total = 1 / 56 probability of chosing jose first = 1 / 8 probability of chosing josh second = 1 / 7 total = 1 / 56 final = 1 / 56 + 1 / 56 = 1 / 28 c"
Answer: c
Question (general): what is the units digit of 63 ^ 3 * 17 ^ 3 * 49 ^ 3 ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: "the units digit of 63 ^ 3 is the units digit of 3 * 3 * 3 = 27 which is 7 . the units digit of 17 ^ 3 is the units digit of 7 * 7 * 7 = 343 which is 3 . the units digit of 49 ^ 3 is the units digit of 9 * 9 * 9 = 729 which is 9 . the units digit of 7 * 3 * 9 = 189 is 9 . the answer is e ."
Answer: e
Question (probability): what is the probability of randomly selecting an arrangement of the letters of the word ` ` mediterranean ' ' in which the first letter is e and the last letter is r ?
Options: a ) 1 / 13 , b ) 1 / 20 , c ) 1 / 26 , d ) 1 / 50 , e ) 1 / 100
Rationale: there are 13 letters in mediterranean , out of which e appears thrice , n appears twice , a appears twice , and r appears twice . the number of arrangements of mediterranean is therefore 13 ! / 3 ! 2 ! 2 ! 2 ! the number of arrangements in which the first letter is e and the last letter is r is 11 ! / 2 ! 2 ! 2 ! ( we are left with 11 letters out of which e appears twice , n appears twice and a appears twice ) . p = ( 11 ! / 2 ! 2 ! 2 ! ) / ( 13 ! / 3 ! 2 ! 2 ! 2 ! ) = 11 / ! 2 ! 2 ! 2 ! ∗ 3 ! 2 ! 2 ! 2 ! / 13 ! = 3 ! / 12 ∗ 13 = 1 / 26 answer : c .
Answer: c
Question (geometry): 10 business executives and 3 chairmen meet at a conference . if each business executive shakes the hand of every other business executive and every chairman once , and each chairman shakes the hand of each of the business executives but not the other chairmen , how many handshakes would take place ?
Options: a ) 144 , b ) 131 , c ) 115 , d ) 90 , e ) 75
Rationale: "there are 10 business exec and in each handshake 2 business execs are involved . hence 10 c 2 = 45 also , each of 10 exec will shake hand with every 3 other chairmen for total of 30 handshake . total = 45 + 30 = 75 ans : e"
Answer: e
Question (physics): a goods train runs at a speed of 72 kmph and crosses a 280 m long platform in 26 seconds . what is the length of the goods train ?
Options: a ) 230 m , b ) 240 m , c ) 260 m , d ) 270 m , e ) 250 m
Rationale: "s = 280 + x / t 72 * 5 / 18 = 280 + x / 26 x = 240 answer : b"
Answer: b