Cheukting/mathqa huggingface dataset:
Question (general): the average of 7 consecutive numbers a , b , c , d , e , f and g is 9 . what percent of g is a ?
Options: a ) 42.0 , b ) 48.0 , c ) 50.0 , d ) 52.2 , e ) 54.0
Rationale: explanation : in such a case the middle number ( d ) is the average ∴ d = 9 and a = 6 and g = 12 required percentage = 6 / 12 x 100 = 50.0 answer : option c
Answer: c
Question (other): a hen leaps 6 leaps for every 8 leaps of a duck , but 4 leaps of the duck are equal to 3 leaps of the hen . what is the ratio of the speed of the hen to that of the duck ?
Options: a ) 1 : 1 , b ) 3 : 8 , c ) 4 : 3 , d ) 8 : 9 , e ) 1 : 3
Rationale: given ; 4 duck = 3 hen ; or , duck / hen = 3 / 4 ; let hen ' s 1 leap = 4 meter and ducks 1 leap = 3 meter . then , ratio of speed of hen and duck = 4 * 6 / 3 * 8 = 1 : 1 ' ' answer : 1 : 1 ;
Answer: a
Question (physics): amar takes as much time in running 24 meters as a car takes in covering 60 meters . what will be the distance covered by amar during the time the car covers 2.2 km ?
Options: a ) 700 m , b ) 500 m , c ) 870 m , d ) 880 m , e ) 840 m
Rationale: "distance covered by amar = 24 / 60 ( 2.2 km ) = 2 / 5 ( 2200 ) = 880 m answer : d"
Answer: d
Question (gain): of the 600 residents of clermontville , 35 % watch the television show island survival , 40 % watch lovelost lawyers and 50 % watch medical emergency . if all residents watch at least one of these 3 shows and 18 % watch exactly 2 of these shows , then how many clermontville residents b watch all of the shows ?
Options: a ) 150 , b ) 108 , c ) 42 , d ) 21 , e ) - 21
Rationale: oa is d . 100 = a + b + c - ab - ac - bc + abc , which is the same as the following formula 100 = a + b + c + ( - ab - ac - bc + abc + abc + abc ) - 2 abc . the term between parantheses value 18 % so the equation to resolve is 100 = 35 + 40 + 50 - 18 - 2 abc therefore the value of abc is 3.5 % of 600 , b is 21 . d is the correct answer
Answer: d
Question (general): the product of two numbers is 336 and the sum of their squares is 289 . the sum of the number is ?
Options: a ) a ) 23 , b ) b ) 25 , c ) c ) 27 , d ) d ) 31 , e ) e ) 35
Rationale: "let the numbers be x and y . then , xy = 336 and x 2 + y 2 = 289 . ( x + y ) 2 = x 2 + y 2 + 2 xy = 289 + ( 2 x 336 ) = 961 x + y = 31 . option d"
Answer: d
Question (physics): the length of a room is 5.5 m and width is 3.75 m . find the cost of paying the floor by slabs at the rate of rs . 600 per sq . metre .
Options: a ) rs . 15,000 , b ) rs . 15,500 , c ) rs . 12,375 , d ) rs . 16,500 , e ) none
Rationale: "solution area of the floor = ( 5.5 x 3.75 ) m ² = 20.635 m ² cost of paying = rs . ( 600 x 20.625 ) = rs . 12,375 . answer c"
Answer: c
Question (physics): x and y together can completes a work in 12 days and y complete the same work in 24 days . then the number of days x required to complete the work will be ?
Options: a ) 15 days . , b ) 12 days . , c ) 24 days . , d ) 13 days . , e ) 16 days .
Rationale: x and y complete in one day = 1 / 12 part , y completes in one day = 1 / 24 parts . therefore x alone can do in one day = 1 / 24 part . therefore the work can be finished by x = 24 days . ans : c
Answer: c
Question (general): if 204 ÷ 12.75 = 16 , then 2.04 ÷ 1.275 = ?
Options: a ) 16 , b ) 1.6 , c ) 0.16 , d ) 0.016 , e ) none of these
Rationale: explanation : ( 204 / 12.75 ) = 16 ⇒ ( 20.4 ) / ( 1.275 ) = 16 ( ∵ divided numerator and denominator by 10 ) ⇒ 2.04 / 1.275 = 1.6 ( ∵ divided lhs and rhs by 10 ) answer : option b
Answer: b
Question (general): if n is an integer and 101 n ^ 2 is less than or equal to 3600 , what is the greatest possible value of n ?
Options: a ) 7 , b ) 5 , c ) 9 , d ) 10 , e ) 11
Rationale: "101 * n ^ 2 < = 3600 n ^ 2 < = 3600 / 101 which will be less than 81 since 3600 / 100 = 36 which is the square of 9 next closest value of n where n ^ 2 < = 36 is 5 ans b"
Answer: b
Question (other): the simple form of the ratio 4 / 3 : 3 / 7 is ?
Options: a ) 7 : 3 , b ) 10 : 3 , c ) 15 : 3 , d ) 25 : 3 , e ) 30 : 3
Rationale: "4 / 3 : 3 / 7 = 21 : 9 = 7 : 3 answer : a"
Answer: a
Question (gain): each month , after jill pays for rent , utilities , food , and other necessary expenses , she has one fifth of her net monthly salary left as discretionary income . of this discretionary income , she puts 30 % into a vacation fund , 20 % into savings , and spends 35 % on eating out and socializing . this leaves her with $ 105 dollar , which she typically uses for gifts and charitable causes . what is jill ’ s net monthly salary ?
Options: a ) $ 2400 , b ) $ 3200 , c ) $ 3500 , d ) $ 6400 , e ) $ 9600
Rationale: let x be the monthly salary 15 % of 1 / 5 * x = 105 x = 3500 answer c
Answer: c
Question (gain): what is 12 percent of 80 ?
Options: a ) 11.21 , b ) 9.6 , c ) 8.66 , d ) 12.23 , e ) 13.1
Rationale: "we assume that 80 is 100 % assume ' x ' is value we looking for here , 80 = 100 % and x = 12 % therefore , 80 / x = 100 % / 12 % 80 / x = 8.33 x = 9.6 b"
Answer: b
Question (general): if the average ( arithmetic mean ) of 5 b , 6 b + 47 b , 8 b - 4 and 2 b is 140 , what is the value of b ?
Options: a ) 20 , b ) 22 , c ) 25 , d ) 30 , e ) 48
Rationale: am of 5 b , 6 b + 47 b , 8 b - 4 and 2 b = 5 b + 6 b + 4 + 7 b + 8 b - 4 + 2 b = 28 b / 5 given that 28 b / 5 = 140 b = 25 answer is c
Answer: c
Question (geometry): you buy a piece of land with an area of â ˆ š 400 , how long is one side of the land plot ?
Options: a ) 28 , b ) 29 , c ) 30 , d ) 20 , e ) 32
Rationale: "try filling the numbers into the answer y x y = find the closest to 400 . answer d"
Answer: d
Question (general): find the number , difference between number and its 3 / 5 is 62 .
Options: a ) 150 , b ) 153 , c ) 154 , d ) 155 , e ) 156
Rationale: "explanation : let the number = x , then , x - ( 3 / 5 ) x = 62 , = > ( 2 / 5 ) x = 62 = > 2 x = 62 * 5 , = > x = 155 answer : option d"
Answer: d
Question (gain): company kw is being sold , and both company a and company b were considering the purchase . the price of company kw is 90 % more than company a has in assets , and this same price is also 100 % more than company b has in assets . if companies a and b were to merge and combine their assets , the price of company kw would be approximately what percent of these combined assets ?
Options: a ) 66 % , b ) 75 % , c ) 86 % , d ) 97 % , e ) 150 %
Rationale: "let the price of company a ' s assets be 100 price of assets of kw is 90 % more than company a ' s assets which is 190 price of assets of kw is 100 % more than company b ' s assets which means price of company b ' s assets is half the price of kw = 95 a + b = 195 kw = 190 kw / ( a + b ) * 100 = 190 / 195 * 100 = 97.43 % or 97 % d"
Answer: d
Question (gain): if $ 200 invested at a certain rate of simple interest amounts to $ 240 at the end of 3 years , how much will $ 150 amount to at the same rate of interest in 6 years ?
Options: a ) $ 190 , b ) $ 180 , c ) $ 200 , d ) $ 240 , e ) $ 210
Rationale: "200 amounts to 240 in 3 years . i . e ( principal + interest ) on 120 in 3 years = 240 200 + 200 * ( r / 100 ) * ( 3 ) = 240 = > r = 20 / 3 150 in 6 years = principal + interest = 150 + 150 * ( r / 100 ) * ( 6 ) = 210 answer is e ."
Answer: e
Question (gain): a man sold 20 articles for $ 60 and gained 20 % . how many articles should he sell for $ 60 to incur a loss 20 % ?
Options: a ) 30 , b ) 36 , c ) 40 , d ) 50 , e ) 48
Rationale: "production cost per article : $ 60 * ( 100 % - 20 % ) / 20 = $ 2.40 required production costs for a loss of 20 % : $ 60 * ( 100 % + 20 % ) = $ 72 number of articles to be sold for $ 72 to incur a 20 % loss : $ 72 / $ 2.40 = 30 thus , solution a is correct ."
Answer: a
Question (physics): a train 200 m long crosses a platform 200 m long in 40 sec ; find the speed of the train ?
Options: a ) 94 kmph , b ) 58 kmph , c ) 54 kmph , d ) 94 kmph , e ) 36 kmph
Rationale: "d = 200 + 200 = 400 t = 40 s = 400 / 40 * 18 / 5 = 36 kmph answer : e"
Answer: e
Question (gain): a shopkeeper sold 30 articles at the cost price of 25 articles . then find the profit % or lost %
Options: a ) 15 % , b ) 18 % , c ) 20 % loss , d ) 25 % , e ) 30 %
Rationale: "here 30 articles selling price = 25 articles cost price so the difference = 25 - 30 = - 5 % of loss = 5 * 100 / 25 = 20 % correct option is c"
Answer: c
Question (physics): the sum of three consecutive even numbers is 30 . find the middle number of the three ?
Options: a ) 14 , b ) 16 , c ) 18 , d ) 25 , e ) 34
Rationale: "three consecutive even numbers ( 2 p - 2 ) , 2 p , ( 2 p + 2 ) . ( 2 p - 2 ) + 2 p + ( 2 p + 2 ) = 30 6 p = 30 = > p = 5 . the middle number is : 5 p = 25 . answer : d"
Answer: d
Question (general): if x is the median of the set { 9 / 2 , 10 / 3 , 27 / 9 , 21 / 5 , x } , x could be
Options: a ) 16 / 5 , b ) 17 / 5 , c ) 28 / 7 , d ) 30 / 7 , e ) 31 / 7
Rationale: "the median is the middle number once all the numbers are arranged in increasing / decreasing order . we see that 10 / 3 = 3 . something , 27 / 9 = 3 . something 21 / 5 = 4 . something 9 / 2 = 4 . something so x should greater than the smallest two numbers and smaller than the greatest two numbers . we can see that x = 4 is possible . ( first look at the simplest option or the middle option since options are usually arranged in increasing / decreasing order ) answer ( c )"
Answer: c
Question (physics): james and david work at a grocery shop with 12 other workers . for an internal review , 2 of the 12 workers will be randomly chosen to be interviewed . what is the probability that james and david will both be chosen ?
Options: a ) 1 / 26 , b ) 1 / 36 , c ) 1 / 46 , d ) 1 / 66 , e ) 1 / 56
Rationale: probability that james and david will both be chosen out of 12 workers = ( 2 / 12 ) * ( 1 / 11 ) = 1 / 66 answer d
Answer: d
Question (general): bookman purchased 40 copies of a new book released recently , 10 of which are hardback and sold for $ 20 each , and rest are paperback and sold for $ 10 each . if 14 copies were sold and the total value of the remaining books was 300 , how many paperback copies were sold ?
Options: a ) 6 , b ) 4 , c ) 8 , d ) 10 , e ) 12
Rationale: "the bookman had 10 hardback ad 40 - 10 = 30 paperback copies ; 14 copies were sold , hence 40 - 14 = 26 copies were left . let # of paperback copies left be p then 10 p + 20 ( 26 - p ) = 300 - - > 10 p = 220 - - > p = 22 # of paperback copies sold is 30 - 22 = 8 answer : c"
Answer: c
Question (gain): a candidate got 35 % of the votes and lost to the rival by 1800 votes . how many votes were cast ?
Options: a ) 5500 , b ) 6000 , c ) 6500 , d ) 7000 , e ) 7500
Rationale: "35 % - - - - - - - - - - - l 65 % - - - - - - - - - - - w - - - - - - - - - - - - - - - - - - 30 % = 1800 10 % = 600 100 % of the votes = 6000 answer : b"
Answer: b
Question (other): a company conducted a survey about its two brands , a and b . x percent of respondents liked product a , ( x – 20 ) percent liked product b , 23 percent liked both products , and 23 percent liked neither product . what is the minimum number d of people surveyed by the company ?
Options: a ) 46 , b ) 80 , c ) d . 90 , d ) d . 100 , e ) 200
Rationale: 100 = x + x - 20 + 23 - 23 x = 60 , so , product a = 60 % , product b = 40 % , both = 23 % , neither = 23 % 23 % of the total no . of people should be an integer . so , a , bc are out . 60 % of d and 40 % of d are both integers . so , d satisfies all conditions . so , answer is d .
Answer: d
Question (general): two trains of equal length are running on parallel lines in the same directions at 46 km / hr . and 36 km / hr . the faster trains pass the slower train in 54 seconds . the length of each train is :
Options: a ) 82 m , b ) 50 m , c ) 75 m , d ) 80 m , e ) none of these
Rationale: "explanation : the relative speed of train is 46 - 36 = 10 km / hr = ( 10 x 5 ) / 18 = 25 / 9 m / s 10 × 518 = 259 m / s in 54 secs the total distance traveled is 54 x 25 / 9 = 150 m . therefore the length of each train is = 150 / 2 = 75 m . answer c"
Answer: c
Question (physics): if 11.25 m of a uniform steel rod weighs 42.75 kg . what will be the weight of 7 m of the same rod ?
Options: a ) 22.8 kg , b ) 26.6 kg , c ) 28 kg , d ) 26.5 kg , e ) none of these
Rationale: "explanation : let the required weight be x kg . then , less length , less weight ( direct proportion ) = > 11.25 : 7 : : 42.75 : x = > 11.25 x x = 7 x 42.75 = > x = ( 7 x 42.75 ) / 11.25 = > x = 26.6 answer : b"
Answer: b
Question (physics): if a farmer wants to plough a farm field on time , he must plough 160 hectares a day . for technical reasons he ploughed only 85 hectares a day , hence he had to plough 2 more days than he planned and he still has 40 hectares left . what is the area of the farm field and how many days the farmer planned to work initially ?
Options: a ) 600 , b ) 490 , c ) 448 , d ) 435 , e ) 679
Rationale: "let x be the number of days in the initial plan . therefore , the whole field is 160 â ‹ … x hectares . the farmer had to work for x + 2 days , and he ploughed 85 ( x + 2 ) hectares , leaving 40 hectares unploughed . then we have the equation : 160 x = 85 ( x + 2 ) + 40 75 x = 210 x = 2.8 so the farmer planned to have the work done in 6 days , and the area of the farm field is 160 ( 2.8 ) = 448 hectares correct answer c"
Answer: c
Question (gain): a chemist mixes one liter of pure water with x liters of a 60 % salt solution , and the resulting mixture is a 10 % salt solution . what is the value of x ?
Options: a ) 1 / 5 , b ) 1 / 3 , c ) 1 / 2 , d ) 1 , e ) 3
Rationale: "concentration of salt in pure solution = 0 concentration of salt in salt solution = 60 % concentration of salt in the mixed solution = 10 % the pure solution and the salt solution is mixed in the ratio of - - > ( 60 - 10 ) / ( 10 - 0 ) = 5 / 1 1 / x = 5 / 1 x = 1 / 5 answer : a"
Answer: a
Question (general): tom reads at an average rate of 30 pages per hour , while jan reads at an average rate of 36 pages per hour . if tom starts reading a novel at 4 : 00 , and jan begins reading an identical copy of the same book at 4 : 48 , at what time will they be reading the same page ?
Options: a ) 7 : 18 , b ) 7 : 48 , c ) 8 : 18 , d ) 8 : 48 , e ) 9 : 18
Rationale: "since tom reads an average of 1 page every 2 minutes , tom will read 24 pages in the first 48 minutes . jan can catch tom at a rate of 6 pages per hour , so it will take 4 hours to catch tom . the answer is d ."
Answer: d
Question (other): bhatia , ashtikar and singh begin to play with rs 70 each . at the end the ratio of the amounts left with ashtikar and singh is 1 : 2 and of those with singh and bhatia is 4 : 1 . what is singh ' s gain ( in rs ) ?
Options: a ) 40 , b ) 45 , c ) 48 , d ) 50 , e ) 53
Rationale: we have b + a + s = 210 and s = 2 a , s = 4 b and a = 2 b solving these eqs we got that singh have rs . 120 in the end bhatia have 30 and astikar have 60 . so singh ' s profit is 120 - 70 = 50 answer : d
Answer: d
Question (general): if x ^ 2 + ( 1 / x ^ 2 ) = 7 , x ^ 4 + ( 1 / x ^ 4 ) = ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 14 , e ) 47
Rationale: "- > x ^ 4 + ( 1 / x ^ 4 ) = ( x ^ 2 ) ^ 2 + ( 1 / x ^ 2 ) ^ 2 = ( x ^ 2 + 1 / x ^ 2 ) ^ 2 - 2 x ^ 2 ( 1 / x ^ 2 ) = 7 ^ 2 - 2 = 47 . thus , the answer is e ."
Answer: e
Question (geometry): the floor of a rectangular room is 19 m long and 12 m wide . the room is surrounded by a veranda of width 2 m on all its sides . the area of the veranda is :
Options: a ) 144 m 2 , b ) 140 m 2 , c ) 108 m 2 , d ) 158 m 2 , e ) none of these
Rationale: "area of the outer rectangle = 23 ã — 16 = 368 m 2 area of the inner rectangle = 19 ã — 12 = 228 m 2 required area = ( 368 â € “ 228 ) = 140 m 2 answer b"
Answer: b
Question (gain): the price of a tv was increased by 30 percent . the new price was then increased by 20 percent . a single increase of what percent is equivalent to these two successive increases ?
Options: a ) 50 % , b ) 60 % , c ) 65 % , d ) 56 % , e ) 45 %
Rationale: consider base price - $ 100 25 % increase = 1.30 * 100 = $ 130 another 20 % increase on new price = 1.2 * 130 = $ 156 so final price of radio - $ 156 therefore a 56 % increase correct option - d
Answer: d
Question (general): simplify : 500 x 500 - 200 x 200
Options: a ) 761200 , b ) 761400 , c ) 761800 , d ) 210000 , e ) none of them
Rationale: "( 500 ) ^ 2 - ( 200 ) ^ 2 = ( 500 + 200 ) ( 500 - 200 ) = 700 x 300 = 210000 . answer is d ."
Answer: d
Question (gain): a man took a loan at rate of 12 % per annum simple interest . after 3 years he had to pay 4320 interest . the principal amount borrowed by him was .
Options: a ) rs 14000 , b ) rs 15000 , c ) rs 12000 , d ) rs 17000 , e ) none of these
Rationale: "explanation : s . i . = p â ˆ — r â ˆ — t / 100 = > p = s . i . â ˆ — 100 / r â ˆ — t = > p = 4320 â ˆ — 100 / 12 â ˆ — 3 = rs 12000 option c"
Answer: c
Question (general): a total of 30 percent of the geese included in a certain migration study were male . if some of the geese migrated during the study and 10 percent of the migrating geese were male , what was the ratio of the migration rate for the male geese to the migration rate for the female geese ? [ migration rate for geese of a certain sex = ( number of geese of that sex migrating ) / ( total number of geese of that sex ) ]
Options: a ) 1 / 4 , b ) 7 / 12 , c ) 2 / 3 , d ) 7 / 27 , e ) 8 / 7
Rationale: "let ' take the number of geese to be 100 . male = 30 . female = 70 . now the second part of the q , let ' s take the number migrated to be 20 . so we have 20 geese that migrated and out of that 10 % are male i . e 10 / 100 * 20 = 2 geese ( males ) and now we know out of the total 20 geese , 2 are male , then 18 have to be female . now the ratio part , male geese ratios = 2 / 30 = 1 / 15 . - a female geese ratios = 18 / 70 = 9 / 35 - b cross multiply equations a and b and you get = 7 / 27 . ans d"
Answer: d
Question (general): of 64 players on a cricket team , 37 are throwers . the rest of the team is divided so one third are left - handed and the rest are right handed . assuming that all throwers are right handed , how many right - handed players are there total ?
Options: a ) 54 , b ) 55 , c ) 59 , d ) 71 , e ) 92
Rationale: "total = 64 thrower = 37 rest = 64 - 37 = 27 left handed = 27 / 3 = 9 right handed = 18 if all thrower are right handed then total right handed is 37 + 18 = 55 so b . 55 is the right answer"
Answer: b
Question (physics): pipe a can fill a tank in 30 minutes . pipe b can fill the same tank 6 times faster than pipe a . if both the pipes are connected to the tank so that they fill the tank simultaneously , how long will it take for the empty tank to overflow ?
Options: a ) 4 minutes , b ) 15 / 4 minutes , c ) 192 / 7 minutes , d ) 224 / 7 minutes , e ) 28 minutes
Rationale: "pipe a can fill a tank in 30 minutes - - > the rate of a = 1 / 30 tank / minute ; pipe b can fill the same tank 6 times fasterthan pipe a - - > the rate of b = 1 / 30 + 6 / 30 = 7 / 30 tank / minute . their combined rate = 1 / 30 + 7 / 30 = 4 / 15 tank / minute ; therefore , a and b can fill the tank in 15 / 4 minutes . answer : b"
Answer: b
Question (physics): if a , b and c together can finish a piece of work in 4 days . a alone in 12 days and b in 9 days , then c alone can do it in ?
Options: a ) 11 , b ) 17 , c ) 18 , d ) 19 , e ) 16
Rationale: "c = 1 / 4 - 1 / 12 – 1 / 9 = 1 / 18 = > 18 days ' answer : c"
Answer: c
Question (gain): michelle deposited a certain sum of money in a savings account on july 1 st , 2007 . she earns an 6.4 % interest compounded semiannually . the sum of money in the account on december 31 st , 2009 is approximately what percent of the initial deposit ?
Options: a ) 117 % , b ) 120 % , c ) 121 % , d ) 135 % , e ) 140 %
Rationale: since michelle earns 6.4 % interest compounded semiannually , then she earns 3.2 % interest every 6 months . now , the simple interest earned in 5 periods ( 30 months = 5 * 6 months ) would be 3.2 % * 5 = 16 % . but , since the interest iscompoundedevery 6 months , then there would be interest earned on interest ( very small amount ) thus the actual interest earned would be a little bit more than 16 % , only answer choice a fits . answer : a
Answer: a
Question (gain): a certain maroon paint contains 50 percent blue pigment and 50 percent red pigment by weight . a certain green paint contains 30 percent blue pigment and 70 percent yellow pigment . when these paints are mixed to produce a brown paint , the brown paint contains 40 percent blue pigment . if the brown paint weighs 10 grams , then the red pigment contributes how many grams of that weight ?
Options: a ) 3 , b ) 3.5 , c ) 2.5 , d ) 4 , e ) 4.5
Rationale: 10 grams of combined mixture and 40 % blue pigment means that the mixtures were mixed 50 % each . thus 5 grams a piece . out of the 5 grams of the dark blue paint , 60 % is red . therefore , 5 * . 5 = 2.5 grams of red pigment
Answer: c
Question (general): chris age after 15 years will be 5 times his age 5 years back . what is the present age of chris ?
Options: a ) 20 , b ) 25 , c ) 15 , d ) 22 , e ) 10
Rationale: "chris present age = x after 15 years = x + 15 5 years back = x - 5 x + 15 = 5 ( x - 5 ) x = 10 answer is e"
Answer: e
Question (physics): a can do a work in 14 days and working together a and b can do the same work in 10 days . in what time can b alone do the work ?
Options: a ) 25 days , b ) 30 days , c ) 23 days , d ) 35 days , e ) 45 days
Rationale: work done by b in 1 day = 1 / 10 - 1 / 14 = ( 7 - 5 ) / 70 = 1 / 35 so , b alone can do the work in 35 days . answer : d
Answer: d
Question (general): if the average of 5 positive integers is 45 and the difference between the largest and the smallest of these 5 numbers is 10 , what is the maximum value possible for the largest of these 5 integers ?
Options: a ) 50 , b ) 53 , c ) 49 , d ) 48 , e ) 44
Rationale: "sum of 5 integer ( a , b , c , d , e ) = 5 * 45 = 225 e - a = 10 i . e . e = a + 10 for e to be maximum remaining 4 must be as small as possible since smallest of 5 numbers is a so to minimize other numbers we can take them equal to the smallest of 5 numbers i . e . a + a + a + a + ( a + 10 ) = 225 i . e . 5 a = 215 i . e . a = 43 i . e . largest e = 43 + 10 = 53 answer : option b"
Answer: b
Question (general): find the lowest common multiple of 24 , 30 and 40 .
Options: a ) 360 , b ) 420 , c ) 120 , d ) 320 , e ) 280
Rationale: "lcm = 2 * 2 * 2 * 3 * 5 = 120 . answer is c"
Answer: c
Question (general): a certain number when divided by 39 leaves a remainder 15 , what is the remainder when the same number is divided by 13 ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 6 , e ) 2
Rationale: "explanation : 39 + 15 = 54 / 13 = 2 ( remainder ) answer : e"
Answer: e
Question (physics): a cistern can be filled by a tap in 5 hours while it can be emptied by another tap in 8 hours . if both the taps are opened simultaneously , then after how much time will the cistern get filled ?
Options: a ) 5.2 hrs , b ) 13.3 hrs , c ) 1.9 hrs , d ) 7.2 hrs , e ) 1.4 hrs
Rationale: "net part filled in 1 hour = ( 1 / 5 - 1 / 8 ) = 3 / 40 the cistern will be filled in 40 / 3 hrs i . e . , 13.3 hrs . answer : b"
Answer: b
Question (general): a , b , and c are integers and a < b < c . s is the set of all integers from a to b , inclusive . q is the set of all integers from b to c , inclusive . the median of set s is ( 3 / 4 ) * b . the median of set q is ( 4 / 8 ) * c . if r is the set of all integers from a to c , inclusive , what fraction of c is the median of set r ?
Options: a ) 2 / 5 , b ) 1 / 2 , c ) 11 / 16 , d ) 5 / 7 , e ) 3 / 4
Rationale: "the answer isc : 11 / 16 . the key to this problem is remembering that the median for a consecutive set of numbers is equivalent to its mean . for example , the mean and median of a set consisting of x , x + 1 , x + 2 , . . . , y will always be ( x + y ) / 2 . for set s , consisting of numbers ( a , a + 1 , . . . , b ) , the median is given to be 3 / 4 * b : ( a + b ) / 2 = ( 3 / 4 ) * b a = b / 2 for set q , consisting of numbers ( b , b + 1 , . . . , c ) , the median is given to be 4 / 8 * c : ( b + c ) / 2 = ( 4 / 8 ) * c b = 0 for set r , consisting of numbers ( a , a + 1 , . . . c ) , the median needs to be found : a = b / 2 = ( 0 ) / 2 = 0 median = ( a + c ) / 2 = ( 0 + c ) / 2 = c / 2 = ( 1 / 2 ) * c ( answer b )"
Answer: b