Cheukting/mathqa huggingface dataset:
Question (general): n = 1 ! + 2 ! + 3 ! . . . . . + 10 ! . what is the last digit of n ^ n ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: as you see 5 ! till 10 ! each unit digit is zero . so 1 ! + 2 ! + 3 ! + 4 ! = 33 so unit digit 3 + 0 = 3 n = 3 n ^ n = 3 ^ 3 = 27 so last digit is 7 . answer : e
Answer: e
Question (gain): by weight , liquid x makes up 0.8 percent of solution a and 1.8 percent of solution b . if 250 grams of solution a are mixed with 700 grams of solution b , then liquid x accounts for what percent of the weight of the resulting solution ?
Options: a ) 1.46 % , b ) 1.93 % , c ) 10 % , d ) 15 % , e ) 19 %
Rationale: i think there is a typo in question . it should have been ` ` by weight liquid ' x ' makes up . . . . . ` ` weight of liquid x = 0.8 % of weight of a + 1.8 % of weight of b when 250 gms of a and 700 gms of b is mixed : weight of liquid x = ( 0.8 * 250 ) / 100 + ( 1.8 * 700 ) / 100 = 14.6 gms % of liquid x in resultant mixture = ( 14.6 / 1000 ) * 100 = 1.46 % a
Answer: a
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 3 , while all other numbers remain the same , what is the new average of set s ?
Options: a ) 6.5 , 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 3 then total increased to 62 + 3 = 65 new avg - 65 / 10 = 6.5 . hence answer is a ."
Answer: a
Question (gain): a is a working partner and b is a sleeping partner in a business . a puts in 20,000 and b 90,000 . a gets 20 % of the profit for managing the business , and the rest is divided in proportion to their capitals . find the share of b in profit of 11000 .
Options: a ) 3500 , b ) 7200 , c ) 6800 , d ) 4800 , e ) none of these
Rationale: "the amount a gets for managing = 20 % of rs . 11000 = 2200 remaining profit = 11000 – 2200 = 8800 this is to be divided in the ratio 2 : 9 . share of b = 9 / 11 of 8800 = 7200 answer b"
Answer: b
Question (other): a group of people participate in some curriculum , 30 of them practice yoga , 25 study cooking , 15 study weaving , 6 of them study cooking only , 8 of them study both the cooking and yoga , 7 of them participate all curriculums . how many people study both cooking and weaving ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "both cooking and weaving = 25 - ( 6 + 8 + 7 ) = 4 so , the correct answer is d ."
Answer: d
Question (geometry): a carpenter constructed a rectangular sandbox with a capacity of 10 cubic feet . if the carpenter were to make a similar sandbox twice as long , twice as wide , and twice as high as the first sandbox , what would be the capacity , in cubic feet , of the second sandbox ?
Options: a ) 20 , b ) 40 , c ) 60 , d ) 80 , e ) 100
Rationale: "a quick note on doubling . when you double a length you have 2 * l 1 . when you double all lengths of a rectangle you have ( 2 * l 1 ) ( 2 * l 2 ) = a . an increase of 2 ^ 2 or 4 . when you double all lengths of a rectangular prism you have ( 2 * l 1 ) ( 2 * l 2 ) ( 2 * l 3 ) = v . an increase of 2 ^ 3 or 8 . this leads to the basic relationship : line : 2 * original size rectangle : 4 * original size rectangular prism : 8 * original size answer is d"
Answer: d
Question (physics): two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 25 kmph and 21 kmph respectively . when they meet , it is found that one train has traveled 60 km more than the other one . the distance between the two stations is ?
Options: a ) 457 km , b ) 444 km , c ) 552 km , d ) 645 km , e ) 453 km
Rationale: "1 h - - - - - 5 ? - - - - - - 60 12 h rs = 25 + 21 = 46 t = 12 d = 46 * 12 = 552 answer : c"
Answer: c
Question (general): 8 , 12 , 18 , 27 , 40.5 , ( . . . )
Options: a ) 62 , b ) 60.75 , c ) 60.5 , d ) 60.25 , e ) 60
Rationale: "8 ( 8 × 3 ) ÷ 2 = 12 ( 12 × 3 ) ÷ 2 = 18 ( 18 × 3 ) ÷ 2 = 27 ( 27 × 3 ) ÷ 2 = 40.5 ( 40.5 × 3 ) ÷ 2 = 60.75 answer is b ."
Answer: b
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 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 ) 75 , b ) 70 , c ) 65 , d ) 85 , e ) 90
Rationale: "let total capacity be x we know 160 = 0.80 x x = 160 / 0.80 = 200 prior to storm , we had 130 bn gallons 200 - 130 = 70 answer : b"
Answer: b
Question (gain): in business , a and c invested amounts in the ratio 2 : 1 , whereas the ratio between amounts invested by a and b was 2 : 5 , if rs 15,000 was their profit , how much amount did b receive .
Options: a ) 1950 , b ) 6895 , c ) 4879 , d ) 8126 , e ) 6250
Rationale: "explanation : a : b = 2 : 5 = 2 : 5 = > a : c = 2 : 1 = 2 : 1 = > a : b : c = 6 : 5 : 1 b share = ( 5 / 12 ) * 15000 = 6250 option e"
Answer: e
Question (physics): 10 women can complete a work in 7 days and 10 children take 14 days to complete the work . how many days will 8 women and 12 children take to complete the work ?
Options: a ) 4 , b ) 5 , c ) 7 , d ) 8 , e ) 2
Rationale: "1 women ' s 1 day work = 1 / 70 1 child ' s 1 day work = 1 / 140 ( 8 women + 12 children ) ' s 1 day work = ( 8 / 70 + 12 / 140 ) = 1 / 5 8 women and 4 children will complete the work in 5 days . b"
Answer: b
Question (general): find the remainder of the division ( 3 ^ 50 ) / 7 .
Options: a ) 5 , b ) 3 , c ) 2 , d ) 1 , e ) 7
Rationale: "find the pattern of the remainders after each power : ( 3 ^ 1 ) / 7 remainder 3 ( 3 ^ 2 ) / 7 remainder 2 ( 3 ^ 3 ) / 7 remainder 6 ( 3 ^ 4 ) / 7 remainder 4 ( 3 ^ 5 ) / 7 remainder 5 ( 3 ^ 6 ) / 7 remainder 1 - - > this is where the cycle ends ( 3 ^ 7 ) / 7 remainder 3 - - > this is where the cycle begins again ( 3 ^ 8 ) / 7 remainder 2 continuing the pattern to ( 3 ^ 50 ) / 7 gives us a remainder of 2 final answer : c ) 2"
Answer: c
Question (general): what is the area inscribed by the lines y = 2 , x = 2 , y = 10 - x on an xy - coordinate plane ?
Options: a ) a ) 8 , b ) b ) 10 , c ) c ) 12 , d ) d ) 14 , e ) e ) 18
Rationale: first , let ' s graph the lines y = 2 and x = 2 at this point , we need to find the points where the line y = 10 - x intersects the other two lines . for the vertical line , we know that x = 2 , so we ' ll plug x = 2 into the equation y = 10 - x to get y = 10 - 2 = 8 perfect , when x = 2 , y = 8 , so one point of intersection is ( 28 ) for the horizontal line , we know that y = 2 , so we ' ll plug y = 2 into the equation y = 10 - x to get 2 = 10 - x . solve to get : x = 8 so , when y = 2 , x = 8 , so one point of intersection is ( 82 ) now add these points to our graph and sketch the line y = 10 - x at this point , we can see that we have the following triangle . the base has length 6 and the height is 6 area = ( 1 / 2 ) ( base ) ( height ) = ( 1 / 2 ) ( 6 ) ( 6 ) = 18 answer : e
Answer: e
Question (gain): alex takes a loan of $ 8,000 to buy a used truck at the rate of 9 % simple interest . calculate the annual interest to be paid for the loan amount .
Options: a ) 680 , b ) 700 , c ) 720 , d ) 730 , e ) 750
Rationale: "from the details given in the problem principle = p = $ 8,000 and r = 9 % or 0.09 expressed as a decimal . as the annual interest is to be calculated , the time period t = 1 . plugging these values in the simple interest formula , i = p x t x r = 8,000 x 1 x 0.09 = 720.00 annual interest to be paid = $ 720 answer : c"
Answer: c
Question (general): if n is a positive integer , what is the remainder when ( 4 ^ ( 4 n + 3 ) ) ( 6 ^ n ) is divided by 10 ?
Options: a ) 1 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: "this one took me bout 3 1 / 2 min . just testin numbers and what not . first notice that n is positive . save time by noticing thati worked out one solution where n = 0 only to find that thats not an option : p . 1 - 7 stands for ^ 1 thru 7 1 : 7 * 1 = 7 2 : 7 * 7 = 9 3 : 7 * 9 = 3 4 : 7 * 3 = 1 5 : 7 * 1 = 7 6 : 7 * 7 = 9 7 : 7 * 9 = 3 pattern repeats every @ 5 . notice every ^ 4 or multiple of 4 is always going to be 1 . this is just for future notice for similar problems . so 7 ^ 4 n + 3 - - - > if n = 1 then its ( ( 7 ^ 7 ) * 6 ) ) / 10 which can say is going to be 3 * 8 - - > 18 / 10 - - > r = 8 now from here if id double check just to make sure . 7 ^ 4 ( 2 ) + 3 * 6 ^ 2 - - - > 7 ^ 11 * 36 or we can just say again 7 ^ 11 * 6 ( b / c we are only interested in the units digit ) . since ^ 12 is going to be 1 that means ^ 11 is going to be 3 ( as taken from our pattern ) so again 3 * 6 = 18 / 10 - - - > r = 8 . c or j in this problem ."
Answer: c
Question (gain): the price of an item is discounted 10 percent on day 1 of a sale . on day 2 , the item is discounted another 20 percent , and on day 3 , it is discounted an additional 40 percent . the price of the item on day 3 is what percentage of the sale price on day 1 ?
Options: a ) 28 % , b ) 48 % , c ) 64.8 % , d ) 70 % , e ) 72 %
Rationale: let initial price be 1000 price in day 1 after 10 % discount = 900 price in day 2 after 20 % discount = 720 price in day 3 after 40 % discount = 432 so , price in day 3 as percentage of the sale price on day 1 will be = 432 / 900 * 100 = > 48 % answer will definitely be ( b )
Answer: b
Question (general): the probability that a man will be alive for 10 more yrs is 1 / 3 & the probability that his wife will alive for 10 more yrs is 2 / 5 . the probability that none of them will be alive for 10 more yrs , is
Options: a ) 1 / 2 , b ) 1 , c ) 2 / 3 , d ) 3 / 4 , e ) 2 / 5
Rationale: "sol . required probability = pg . ) x p ( b ) = ( 1 — d x ( 1 — i ) = : x 1 = 2 / 5 ans . ( e )"
Answer: e
Question (geometry): a 9 by 12 rectangle is inscribed in circle . what is the circumference of the circle ?
Options: a ) 2.5 π , b ) 5 π , c ) 10 π , d ) 12.5 π , e ) 15 π
Rationale: "the diagonal of the rectangle will be the diameter of the circle . and perimeter = 2 * pi * r ans : e"
Answer: e
Question (other): each of the dogs in a certain kennel is a single color . each of the dogs in the kennel either has long fur or does not . of the 45 dogs in the kennel , 28 have long fur , 17 are brown , and 8 are neither long - furred nor brown . how many long - furred dogs are brown ?
Options: a ) 26 , b ) 19 , c ) 11 , d ) 8 , e ) 6
Rationale: "no of dogs = 45 long fur = 28 brown = 17 neither long fur nor brown = 8 therefore , either long fur or brown = 45 - 8 = 37 37 = 28 + 17 - both both = 8 answer d"
Answer: d
Question (general): when tossed , a certain coin has equal probability of landing on either side . if the coin is tossed 4 times , what is the probability that it will land twice on heads and twice tails ?
Options: a ) 1 / 8 , b ) 1 / 4 , c ) 1 / 16 , d ) 1 / 32 , e ) 1 / 2
Rationale: must be twice on heads and twice on tails 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 = 1 / 16 answer : c
Answer: c
Question (gain): the effective annual rate of interest corresponding to a nominal rate of 14 % per annum payable half - yearly is ?
Options: a ) 16.06 % , b ) 16.07 % , c ) 16.08 % , d ) 14.49 % , e ) 16.19 %
Rationale: "amount of rs . 100 for 1 year when compounded half - yearly = [ 100 * ( 1 + 7 / 100 ) 2 ] = rs . 14.49 effective rate = ( 114.49 - 100 ) = 14.49 % answer : d"
Answer: d
Question (general): mary ' s income is 60 percent more than tim ' s income , and tim ' s income is 50 percent less than juan ' s income . what percent of juan ' s income is mary ' s income ?
Options: a ) 124 % , b ) 120 % , c ) 96 % , d ) 80 % , e ) 64 %
Rationale: "juan ' s income = 100 ( assume ) ; tim ' s income = 50 ( 50 percent less than juan ' s income ) ; mary ' s income = 80 ( 60 percent more than tim ' s income ) . thus , mary ' s income ( 80 ) is 80 % of juan ' s income ( 100 ) . answer : d ."
Answer: d
Question (general): the circumferences of the fore and hind - wheels of a carriage are 2 2 / 5 and 3 3 / 7 meters respectively . a chalk mark is put on the point of contact of each wheel with the ground at any given moment . how far will the carriage have travelled so that their chalk marks may be again on the ground at the same time ?
Options: a ) 18 metres , b ) 16 metres , c ) 38 metres , d ) 42 metres , e ) 24 metres
Rationale: a little reflection will show that chalk marks will touch the ground together for the first time after the wheels have passed over a distance which is the lcm of 2 2 / 5 metres and 3 3 / 7 metres . lcm of 12 / 5 metres and 24 / 7 metres = 24 metres . answer is e
Answer: e
Question (physics): a can do a piece of work in 5 days and b can do it in 4 days how long will they both work together to complete the work ?
Options: a ) 6 / 11 , b ) 8 / 11 , c ) 7 / 9 , d ) 2 / 9 , e ) 10 / 11
Rationale: "explanation : a ’ s one day work = 1 / 5 b ’ s one day work = 1 / 4 ( a + b ) ’ s one day work = 1 / 5 + 1 / 4 = 9 / 20 = > time = 20 / 9 = 2 2 / 9 days answer : option d"
Answer: d
Question (general): if 5 ^ 5 × 5 ^ x = ( 125 ) ^ 4 , then what is the value of x ?
Options: a ) 2 , b ) 3 , c ) 5 , d ) 6 , e ) 7
Rationale: "5 ^ 5 × 5 ^ x = ( 125 ) ^ 4 5 ^ ( 5 + x ) = 5 ^ 12 since they have the same base we can just set the exponents equal to each other : ( 5 + x ) = 12 x = 7 ans . e ) 7"
Answer: e
Question (general): a 100 - litre mixture of milk and water contains 30.25 litres of milk . ' x ' litres of this mixture is removed and replaced with an equal quantum of water . if the process is repeated once , then the concentration of the milk stands reduced at 25 % . what is the value of x ?
Options: a ) 9.1 litres , b ) 10 litres , c ) 8 litres , d ) 12 litres , e ) 6 litres
Rationale: working formula . . . initial concentration * initial volume = final concentration * final volume . let x is the part removed from 100 lts . 30.25 % ( 1 - x / 100 ) ^ 2 = 25 % * 100 % ( 1 - x / 100 ) ^ 2 = 25 / 30.25 - - - - - - > ( 1 - x / 100 ) ^ 2 = ( 5 / 5.5 ) ^ 2 100 - x = 500 / 5.5 x = 9.1 . . . ans a
Answer: a
Question (general): m and n are the x and y coordinates , respectively , of a point in the coordinate plane . if the points ( m , n ) and ( m + p , n + 12 ) both lie on the line defined by the equation x = ( y / 4 ) - ( 2 / 5 ) , what is the value of p ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "x = ( y / 4 ) - ( 2 / 5 ) , and so y = 4 x + 8 / 5 . the slope is 4 . ( n + 12 - n ) / ( m + p - m ) = 3 p = 3 the answer is c ."
Answer: c
Question (physics): 1000 men have provisions for 15 days . if 300 more men join them , for how many days will the provisions last now ?
Options: a ) 11.5 , b ) 12.5 , c ) 12.6 , d ) 12.2 , e ) 12.1
Rationale: "1000 * 15 = 1300 * x x = 11.5 answer : a"
Answer: a
Question (general): the equation of line a is y = 4 / 3 * x - 100 . what is the smallest possible distance in the xy - plane from the point with coordinates ( 0 , 0 ) to any point on line a ?
Options: a ) 48 , b ) 50 , c ) 60 , d ) 75 , e ) 100
Rationale: this can be solve in two steps and without any complex calculation . given : equation of line a as y = ( 4 / 3 ) x - 100 . so the line intercept the axes at ( 0 , - 100 ) and ( 750 ) . this can be considered a right angle triangle with right angle at ( 00 ) . so base = 100 , height = 75 and hypotenuse = 125 ( by pythagoras triplet ) so a perpendicular from the ( 00 ) to hypotenuse will be the answer . area of triangle = 0.5 * 100 * 75 = 0.5 * 125 * x = > x = 60 ; so answer is 60 = c
Answer: c
Question (general): the average age of applicants for a new job is 31 , with a standard deviation of 6 . the hiring manager is only willing to accept applications whose age is within one standard deviation of the average age . what is the maximum number of different ages of the applicants ?
Options: a ) 8 , b ) 13 , c ) 15 , d ) 18 , e ) 30
Rationale: "within one standard deviation of the average age means 31 + / - 7 25 - - 31 - - 37 number of dif . ages - 25 26 27 28 29 30 31 32 33 34 35 36 37 total = 13 b"
Answer: b
Question (physics): 20 men take 21 days of 8 hours each to do a piece of work . how many days of 6 hours each would 21 women take to do the same . if 3 women do as much work as 2 men ?
Options: a ) 32 , b ) 87 , c ) 40 , d ) 99 , e ) 77
Rationale: "3 w = 2 m 20 m - - - - - - 21 * 8 hours 21 w - - - - - - x * 6 hours 14 m - - - - - - x * 6 20 * 21 * 8 = 14 * x * 6 x = 40 answer : c"
Answer: c
Question (general): the class mean score on a test was 40 , and the standard deviation was 15 . if jack ' s score was within 2 standard deviations of the mean , what is the lowest score he could have received ?
Options: a ) 20 , b ) 31 , c ) 45 , d ) 90 , e ) 89
Rationale: "1 sd from the mean is adding and subtrating the amount if standard deviation from the mean one time . 2 sd from the mean is adding and subtracting twice . 1 sd from the mean ranges from 25 to 55 , where 55 is within sd above the mean and 25 within 1 sd below the mean 2 sd = 15 twice = 30 from the the mean , which is 55 to 25 , where 55 is within 2 sd above the mean and 30 is within 2 sd below the mean . answer = a"
Answer: a
Question (gain): machine a produces 100 parts thrice as fast as machine b does . machine b produces 100 parts in 30 minutes . if each machine produces parts at a constant rate , how many parts does machine a produce in 6 minutes ?
Options: a ) 20 , b ) 80 , c ) 40 , d ) 60 , e ) 50
Rationale: machine b produces 100 part in 30 minutes . machine a produces 100 parts thrice as fast as b , so machine a produces 100 parts in 30 / 3 = 10 minutes . now , machine a produces 100 parts in 10 minutes which is 100 / 10 = 10 parts / minute . 10 parts x a total of 6 minutes = 60 d
Answer: d
Question (general): machine x takes 80 hours longer than machine y to produce 1080 widgets . machine y produces 20 percent more widgets in an hour than machine x does in an hour . how many widgets per hour does machine x produce
Options: a ) 100 , b ) 65 , c ) 25 , d ) 11 , e ) 2.25
Rationale: "machine y produces 20 percent more widgets in an hour than machine x does in an hour . so if machine x produces 100 widgets , then machine y produces 120 widgets . ratio of 120 / 100 = 6 / 5 . this is their speed of work ( y : x ) . i . e . speed of their work ( x : y ) = 5 / 6 now , time is inversely proportional to speed . hence the ratio of the time spent ( x : y ) = 6 / 5 let us assume that they spend 6 x and 5 x hours . given that 6 x - 5 x = 80 so , x = 80 . hence 6 x = 6 * 80 = 480 hours . hence x takes 120 hours to produce 1080 widgets . so , in 1 hour , it can produce ( 1 * 1080 ) / 480 = 2.25 hence option ( e ) ."
Answer: e
Question (general): in the faculty of reverse - engineering , 226 second year students study numeric methods , 423 second year students study automatic control of airborne vehicles and 134 second year students study them both . how many students are there in the faculty if the second year students are approximately 80 % of the total ?
Options: a ) 515 , b ) 545 , c ) 618 . , d ) 644 . , e ) 666
Rationale: "solution : total number of students studying both are 423 + 226 - 134 = 515 ( subtracting the 134 since they were included in the both the other numbers already ) . so 80 % of total is 515 , so 100 % is approx . 644 . answer is d : 644"
Answer: d
Question (general): the average of 5 quantities is 9 . the average of 3 of them is 4 . what is the average of remaining 2 numbers ?
Options: a ) 16.5 , b ) 10 , c ) 8 , d ) 9.5 , e ) none of these
Rationale: "answer : a ( 5 x 9 - 3 x 4 ) / 2 = 16.5"
Answer: a
Question (physics): two goods trains each 500 m long are running in opposite directions on parallel tracks . their speeds are 60 km / hr and 30 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one ?
Options: a ) 12 sec , b ) 24 sec , c ) 40 sec , d ) 60 sec , e ) 62 sec
Rationale: "relative speed = 60 + 30 = 90 km / hr . 90 * 5 / 18 = 25 m / sec . distance covered = 500 + 500 = 1000 m . required time = 1000 / 25 = 40 sec . answer : c"
Answer: c
Question (general): the average height of 30 students in a class was calculated as 177 cm . it has later found that the height of one of the students in the class was incorrectly written as 151 cm whereas the actual height was 106 cm . what was the actual average height of the students in the class ?
Options: a ) 176.5 cm , b ) 175.5 cm , c ) 174.5 cm , d ) 173.5 cm , e ) 172.5 cm
Rationale: "the total height was 45 cm too much . the average height should be reduced by 45 cm / 30 = 1.5 cm the answer is b ."
Answer: b
Question (physics): a man is walking at a speed of 10 km per hour . after every kilometre , he takes rest for 6 minutes . how much time will be take to cover a distance of 6 kilometres ?
Options: a ) 48 min . , b ) 50 min . , c ) 66 min . , d ) 55 min . , e ) none of these
Rationale: "rest time = number of rest ã — time for each rest = 5 ã — 6 = 30 minutes total time to cover 6 km = ( 6 â  „ 10 ã — 60 ) minutes + 30 minutes = 66 minutes answer c"
Answer: c
Question (physics): a train 150 m long passes a km stone in 15 seconds and another train of the same length travelling in opposite direction in 8 seconds . the speed of the second train is
Options: a ) 60 kmph , b ) 66 kmph , c ) 72 kmph , d ) 99 kmph , e ) 89 kmph
Rationale: given that two trains are of same length i . e . . 150 mtrs first train passes the km stone in 15 seconds . here we have time and distance so speed = 150 / 15 = 10 m / s we need to find out the second train speed . suppose the speed of the 2 nd train is x m / s relative speed of two trains is ( 10 + x ) = = > ( 150 + 150 ) / ( 10 + x ) = 8 = = > ( 300 ) / ( 10 + x ) = 8 = = > 300 = 80 + 8 x = = > 300 - 80 = 8 x = = > 220 = 8 x : - x = 55 / 2 m / s convert m / s into km / ph ( 55 / 2 ) * ( 18 / 5 ) = 99 kmph answer : d
Answer: d
Question (geometry): what is the max number of rectangular boxes , each measuring 5 inches by 2 inches by 7 inches , that can be packed into a rectangular packing box measuring 15 inches by 20 inches by 35 inches , if all boxes are aligned in the same direction ?
Options: a ) 200 , b ) 350 , c ) 100 , d ) 150 , e ) 120
Rationale: "the 5 inch side should be aligned to the 15 inch side ( 3 layer ) 2 inch side should be aligned to the 20 inch side . ( 10 layer ) 7 inch side should be aligned to the 35 inch side . ( 5 layer ) maximum number of rectangles = 3 * 10 * 5 = 150 answer is d"
Answer: d
Question (gain): the difference between the compound interest compounded annually and simple interest for 2 years at 20 % per annum is rs . 288 . find the principal ?
Options: a ) 2277 , b ) 2667 , c ) 3600 , d ) 7200 , e ) 1811
Rationale: "p = 288 ( 100 / 5 ) ^ 2 = > p = 7200 answer : d"
Answer: d
Question (gain): 63.2 is what percent of 867 ?
Options: a ) 6.9 , b ) 8.99 , c ) 7.29 , d ) 7.98 , e ) 9.21
Rationale: "we assume that 867 is 100 % assume ' x ' is value we looking for here , 867 = 100 % and x % = 63.2 therefore , 100 / x = 867 / 63.2 100 / x = 13.71 x = 7.29 c"
Answer: c
Question (physics): p can do a work in the same time in which q and r together can do it . if p and q work together , the work can be completed in 10 days . r alone needs 15 days to complete the same work . then q alone can do it in
Options: a ) 20 , b ) 22 , c ) 25 , d ) 27 , e ) 60
Rationale: "work done by p and q in 1 day = 1 / 10 work done by r in 1 day = 1 / 15 work done by p , q and r in 1 day = 1 / 10 + 1 / 15 = 1 / 6 but work done by p in 1 day = work done by q and r in 1 day . hence the above equation can be written as work done by p in 1 day ã — 2 = 1 / 6 = > work done by p in 1 day = 1 / 12 = > work done by q and r in 1 day = 1 / 12 hence work done by q in 1 day = 1 / 12 â € “ 1 / 15 = 1 / 60 so q alone can do the work in 60 days answer is e ."
Answer: e
Question (other): local kennel has cats and dogs in the ratio of 6 : 12 . if there are 24 fewer cats than dogs , how many dogs are in the kennel ?
Options: a ) 50 , b ) 48 , c ) 52 , d ) 54 , e ) 56
Rationale: "lets work with the data given to us . we know that there ratio of cats to dogs is 6 : 12 or cats 6 dogs 12 we can write number of cats as 6 x and number of dogs as 12 x and we know that 12 x - 6 x = 24 ( therefore 6 x = 24 = > x = 4 ) then # of dogs = 12 x 4 = 48 answer is b"
Answer: b