Cheukting/mathqa huggingface dataset:
Question (physics): john left home and drove at the rate of 55 mph for 2 hours . he stopped for lunch then drove for another 3 hours at the rate of 55 mph to reach his destination . how many miles did john drive ?
Options: a ) 235 miles . , b ) 245 miles . , c ) 255 miles . , d ) 265 miles . , e ) 275 miles .
Rationale: "the total distance d traveled by john is given by d = 55 * 2 + 3 * 55 = 275 miles . answer e"
Answer: e
Question (geometry): a circular well with a diameter of 4 metres , is dug to a depth of 14 metres . what is the volume of the earth dug out ?
Options: a ) 32 m 3 , b ) 36 m 3 , c ) 40 m 3 , d ) 44 m 3 , e ) 176 m 3
Rationale: "solution volume = π r 2 h ‹ = › ( 22 / 7 × 2 × 2 × 14 ) m 3 ‹ = › 176 m 3 . answer e"
Answer: e
Question (physics): six bells commence tolling together and toll at intervals of 2 , 4,6 , 8,10 and 12 seconds respectively . in 30 m 9 nutes , how many times do they toll together ?
Options: a ) 4 , b ) 10 , c ) 15 , d ) 16 , e ) 17
Rationale: "solution l . c . m . of 2,4 , 6,8 , 10,12 is 120 . so , the bells will toll together after every 120 seconds , i . e . , 2 minutes in 30 minutes , they will toll together left [ ( 30 / 2 ) + 1 ] = 16 times . answer d"
Answer: d
Question (physics): a man cycling along the road noticed that every 6 minutes a bus overtakes him and every 2 minutes he meets an oncoming bus . if all buses and the cyclist move at a constant speed , what is the time interval between consecutive buses ?
Options: a ) 3 minutes , b ) 6 minutes , c ) 8 minutes , d ) 9 minutes , e ) 10 minutes
Rationale: "let ' s say the distance between the buses is d . we want to determine interval = \ frac { d } { b } , where b is the speed of bus . let the speed of cyclist be c . every 6 minutes a bus overtakes cyclist : \ frac { d } { b - c } = 6 , d = 6 b - 6 c ; every 2 minutes cyclist meets an oncoming bus : \ frac { d } { b + c } = 2 , d = 2 b + 2 c ; d = 6 b - 6 c = 2 b + 2 c , - - > b = 2 c , - - > d = 6 b - 3 b = 3 b . interval = \ frac { d } { b } = \ frac { 3 b } { b } = 3 answer : a ( 3 minutes ) ."
Answer: a
Question (geometry): what is the area of a square field whose diagonal of length 30 m ?
Options: a ) 287 , b ) 269 , c ) 450 , d ) 200 , e ) 230
Rationale: "d 2 / 2 = ( 30 * 30 ) / 2 = 450 answer : c"
Answer: c
Question (general): what is the least number should be added to 1056 , so the sum of the number is completely divisible by 25 ?
Options: a ) 19 , b ) 20 , c ) 32 , d ) 41 , e ) 53
Rationale: "( 1056 / 25 ) gives remainder 6 19 + 6 = 23 , so we need to add 19 a"
Answer: a
Question (physics): a rectangular grassy plot 110 m . by 65 m has a gravel path 2.5 m wide all round it on the inside . find the cost of gravelling the path at 50 paise per sq . metre
Options: a ) s 425 , b ) s 780 , c ) s 880 , d ) s 480 , e ) s 980
Rationale: "area of the plot = 110 m * 65 m = 7150 sq . m area of plot excluding gravel = 105 m * 60 m = 6300 sq . m area of gravel = 7150 sq . m - 6300 sq . m = 850 sq . m cost of building it = 850 sq . m * 50 = 42500 p in rs = 42500 / 100 = rs 425 answer : a"
Answer: a
Question (gain): a man bought 40 shares of rs . 60 at 7 discount , the rate of dividend being 1212 % the rate of interest obtained is
Options: a ) 13.64 % , b ) 15.5 % , c ) 14 % , d ) 14.15 % , e ) 14.95 %
Rationale: "explanation : face value of a share = rs . 60 he bought each share at rs . 60 - rs . 7 = rs . 53 number of shares = 40 dividend = 12 1 / 2 % = 25 / 2 % dividend per share = 60 × 25 / 2 × 100 = rs . 7.5 total dividend = ( 40 × 7.5 ) ie , he got a dividend of ( 40 × 7.5 ) for an investment of rs . ( 40 × 53 ) interest obtained = 40 × 7.5 × 100 / 40 × 53 = 14.15 % answer : option d"
Answer: d
Question (geometry): a metallic sheet is of rectangular shape with dimensions 48 m x 36 m . from each of its corners , a square is cut off so as to make an open box . if the length of the square is 8 m , the volume of the box ( in m ^ 3 ) is :
Options: a ) 2130 , b ) 3620 , c ) 4512 , d ) 5620 , e ) 5120
Rationale: "clearly , l = ( 48 - 16 ) m = 32 m , b = ( 36 - 16 ) m = 20 m , h = 8 m . volume of the box = ( 32 x 20 x 8 ) m 3 = 5120 m ^ 3 . answer e"
Answer: e
Question (general): if 853845 bars of chocolate need to be placed in little boxes and each box can contain at most 9 bars of chocolate . how many bars of chocolate will be in the last unfilled box ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 6 , e ) 7
Rationale: the number of bars of chocolate that can be placed in the little boxes of 9 bars is the first number that is divisible by 9 that occurs before 853845 . in order to divide the sum in 9 parts , the amount must be divisible by 9 divisibility rule of 9 : the sum of the digits must be divisible by 9 sum of digits of 853845 = 33 and 27 is divisible by 9 . hence , we need to remove 6 to this number for it to be divisible by 9 correct option : d
Answer: d
Question (physics): the length of a bridge in meters , which a train 110 - meters long and traveling at 45 km / hr can cross in 30 seconds is ?
Options: a ) 245 , b ) 265 , c ) 295 , d ) 325 , e ) 375
Rationale: "45 km / h = 45000 m / 3600 s = 12.5 m / s in 30 seconds , the train can go 30 ( 12.5 ) = 375 meters let x be the length of the bridge . x + 110 = 375 meters x = 265 meters the answer is b ."
Answer: b
Question (other): income and expenditure of a person are in the ratio 9 : 8 . if the income of the person is rs . 36000 , then find his savings ?
Options: a ) 2000 , b ) 3000 , c ) 4000 , d ) 5000 , e ) 6000
Rationale: "let the income and the expenditure of the person be rs . 9 x and rs . 7 x respectively . income , 9 x = 36000 = > x = 4000 savings = income - expenditure = 9 x - 8 x = x so , savings = rs . 4000 . answer : c"
Answer: c
Question (physics): light glows for every 16 seconds . how many times did it between 1 : 57 : 58 and 3 : 20 : 47 am
Options: a ) 311 , b ) 322 , c ) 313 , d ) 314 , e ) 385
Rationale: "the diff in sec between 1 : 57 : 58 and 3 : 20 : 47 is 4969 sec , 4969 / 16 = 310 . so total 311 times light ll glow answer : a"
Answer: a
Question (gain): the difference between c . i . and s . i . on an amount of rs . 15,000 for 2 years is rs . 294 . what is the rate of interest per annum ?
Options: a ) 18 , b ) 12 , c ) 9 , d ) 14 , e ) 16
Rationale: "explanation : [ 15000 * ( 1 + r / 100 ) 2 - 15000 ] - ( 15000 * r * 2 ) / 100 = 294 15000 [ ( 1 + r / 100 ) 2 - 1 - 2 r / 100 ] = 294 15000 [ ( 100 + r ) 2 - 10000 - 200 r ] / 10000 = 294 r 2 = ( 294 * 2 ) / 3 = 196 = > r = 14 rate = 14 % answer : option d"
Answer: d
Question (physics): a thief goes away with a santro car at a speed of 30 kmph . the theft has been discovered after half an hour and the owner sets off in a bike at 60 kmph when will the owner over take the thief from the start ?
Options: a ) 1 hours , b ) 2 hours , c ) 2 / 3 hours , d ) 1 / 3 hours , e ) 2 / 5 hours
Rationale: "- - - - - - - - - - - 30 - - - - - - - - - - - - - - - - - - - - | 60 30 d = 30 rs = 60 â € “ 30 = 30 t = 30 / 30 = 1 hours answer : a"
Answer: a
Question (general): a sum of money is to be distributed among a , b , c , d in the proportion of 5 : 2 : 4 : 3 . if c gets rs . 10000 more than d , what is b ' s share ?
Options: a ) a ) 82390 , b ) b ) 29000 , c ) c ) 20005 , d ) d ) 23930 , e ) e ) 20000
Rationale: "let the shares of a , b , c and d be 5 x , 2 x , 4 x and 3 x rs . respectively . then , 4 x - 3 x = 1000 = > x = 10000 . b ' s share = rs . 2 x = 2 * 10000 = rs . 20000 . answer : e"
Answer: e
Question (gain): one night a certain hotel rented 1 / 2 of its rooms , including 2 / 3 of their air conditioned rooms . if 3 / 5 of its rooms were air conditioned , what percent of the rooms that were not rented were air conditioned ?
Options: a ) 25 % , b ) 30 % , c ) 35 % , d ) 40 % , e ) 50 %
Rationale: "the rooms which were not rented is 1 / 2 the ac rooms which were not rented is ( 1 / 3 ) * ( 3 / 5 ) = 1 / 5 the percentage of unrented rooms which were ac rooms is ( 1 / 5 ) / ( 1 / 2 ) = 2 / 5 = 40 % the answer is d ."
Answer: d
Question (general): a class is 6 meters 24 centimeters in length and 4 meters 32 centimeters in width . find the least number of square tiles of equal size required to cover the entire floor of the class room ?
Options: a ) 115 , b ) 117 , c ) 116 , d ) 114 , e ) 112
Rationale: explanation : length = 6 m 24 cm = 624 cm width = 4 m 32 cm = 432 cm hcf of 624 and 432 = 48 number of square tiles required = ( 624 x 432 ) / ( 48 x 48 ) = 13 x 9 = 117 . answer is b
Answer: b
Question (general): 128 % of 5 / 8 =
Options: a ) 0.2 , b ) 0.5 , c ) 0.6 , d ) 0.8 , e ) 1.0
Rationale: "should be simple . 1.28 * 5 / 8 = 6.4 / 8 = 0.8 correct option : d"
Answer: d
Question (general): mixture contains alcohol and water in the ratio 4 : 3 . if 4 liters of water is added to the mixture , the ratio becomes 4 : 5 . find the quantity of alcohol in the given mixture .
Options: a ) 20 , b ) 99 , c ) 27 , d ) 22 , e ) 29
Rationale: "let the quantity of alcohol and water be 4 x litres and 3 x litres respectively 16 x = 4 ( 3 x + 5 ) 4 x = 20 x = 5 quantity of alcohol = ( 4 x 5 ) litres = 20 litres . answer : a"
Answer: a
Question (general): the sum of the fourth and twelfth term of an arithmetic progression is 20 . what is the sum of the first 12 terms of the arithmetic progression ?
Options: a ) 300 , b ) 120 , c ) 150 , d ) 170 , e ) 270
Rationale: "n th term of a . p . is given by a + ( n - 1 ) d 4 th term = a + 3 d 12 th term = a + 11 d given a + 3 d + a + 11 d = 20 - - > 2 a + 14 d = 20 - - > a + 7 d = 10 sum of n term of a . p = n / 2 [ 2 a + ( n - 1 ) d ] subsitiuing n = 12 . . . we get 12 / 2 [ 2 a + 14 d ] = 15 [ a + 7 d ] = 12 * 10 = 120 . . . answer is b . . ."
Answer: b
Question (gain): sonika bought a v . c . r . at the list price of 18,700 . if the rate of sales tax was 8 % , find the amount she had to pay for purchasing the v . c . r .
Options: a ) 20,196 , b ) 19,780 , c ) 19,680 , d ) 19,380 , e ) none of these
Rationale: "sol . list price of v . c . r . = 18,700 rate of sales tax = 8 % ∴ sales tax = 8 % of 18,700 = 8 ⁄ 100 × 18700 = 1496 so , total amount which sonika had to pay for purchasing the v . c . r . = 18,700 + 1496 = 20,196 . answer a"
Answer: a
Question (physics): if the speed of a man is 54 km per hour , then what is the distance traveled by him in 25 seconds ?
Options: a ) 275 m , b ) 360 m , c ) 375 m , d ) 420 m , e ) 440 m
Rationale: the distance traveled in 25 sec = 54 * ( 5 / 18 ) * 25 = 375 m answer : c
Answer: c
Question (general): soja finished 2 / 3 of a book . she calculated that she finished 100 more pages than she has yet to read . how long is her book ?
Options: a ) a ) 300 , b ) b ) 150 , c ) c ) 130 , d ) d ) 90 , e ) e ) 210
Rationale: let x be the total number of pages in the book , then she finished 2 / 3 * x pages . then she has x − 2 / 3 * x = 1 / 3 * x pages left . 2 / 3 * x − 1 / 3 * x = 100 1 / 3 * x = 100 x = 300 so the book is 300 pages long . answer is a .
Answer: a
Question (physics): a monkey ascends a greased pole 18 metres high . he ascends 2 metres in first minute and slips down 1 metre in the alternate minute . in which minute , he reaches the top ?
Options: a ) 21 st , b ) 22 nd , c ) 33 rd , d ) 24 th , e ) none of these
Rationale: "in 2 minutes , he ascends = 1 metre â ˆ ´ 16 metres , he ascends in 32 minutes . â ˆ ´ he reaches the top in 33 rd minute . answer c"
Answer: c
Question (general): the average score of a cricketer in 10 matches is 60 and in other 15 matches is 70 . then find the average score in all the 25 matches ?
Options: a ) 50 , b ) 48 , c ) 65 , d ) 66 , e ) 72
Rationale: "average in 25 matches = ( 10 * 60 + 15 * 70 ) / 10 + 15 = 66 answer is d"
Answer: d
Question (general): one - third less than 30 % of 180 is equal to :
Options: a ) 15 , b ) 30 , c ) 36 , d ) 40 , e ) 45
Rationale: "lots of ways to tackle this . 30 % of 180 = 54 1 / 3 of 45 = 18 so , 1 / 3 less than 54 is equal to 54 - 18 = 36 answer : c"
Answer: c
Question (general): the average of marks obtained by 120 boys was 35 . if the average of marks of passed boys was 39 and that of failed boys was 15 , the number of boys who passed the examination is ?
Options: a ) 100 , b ) 110 , c ) 120 , d ) 130 , e ) 140
Rationale: "let the number of boys who passed = x . then , 39 x x + 15 x ( 120 - x ) = 120 x 35 24 x = 4200 - 1800 = > x = 2400 / 24 x = 100 . hence , the number of boys passed = 100 . answer : a"
Answer: a
Question (general): a whale goes on a feeding frenzy that lasts for 5 hours . for the first hour he catches and eats x kilos of plankton . in every hour after the first , it consumes 3 kilos of plankton more than it consumed in the previous hour . if by the end of the frenzy the whale will have consumed a whopping accumulated total 450 kilos of plankton , how many kilos did he consume on the third hour ?
Options: a ) 38 , b ) 47 , c ) 50 , d ) 53 , e ) 93
Rationale: "if you list the amount eaten each hour , you ' ll get an equally spaced list , increasing by 3 each hour . in any equally spaced list , the median equals the mean . here , the mean is 450 / 5 = 90 , so the median is also 90 , and that is the amount eaten in the 2 nd hour . we need to add 3 to find the total eaten in the next hour , so the answer is 93 option e"
Answer: e
Question (general): a sum of money is to be distributed among a , b , c , d in the proportion of 5 : 2 : 4 : 3 . if c gets $ 500 more than d , what is b ' s share ?
Options: a ) $ 500 , b ) $ 1000 , c ) $ 1500 , d ) $ 2000 , e ) $ 2500
Rationale: "let the shares of a , b , c and d be 5 x , 2 x , 4 x and 3 x respectively . then , 4 x - 3 x = 500 x = $ 500 b ' s share = 2 x = 2 * $ 500 = $ 1000 the answer is b ."
Answer: b
Question (physics): if 5 spiders make 5 webs in 5 days , then 1 spider will make 1 web in how many days ?
Options: a ) 7 , b ) 6 , c ) 5 , d ) 4 , e ) 3
Rationale: "let the required number days be x . less spiders , more days ( indirect proportion ) less webs , less days ( direct proportion ) spiders 1 : 5 webs 5 : 1 1 x 5 x x = 5 x 1 x 5 = > x = 5 answer is c"
Answer: c
Question (general): 10 camels cost as much as 24 horses , 16 horses cost as much as 4 oxen and 6 oxen as much as 4 elephants . if the cost of 10 elephants is rs . 150000 , find the cost of a camel ?
Options: a ) s . 9800 , b ) s . 3800 , c ) s . 9800 , d ) s . 6000 , e ) s . 6880
Rationale: "cost of the camel = p 10 camels = 24 horses 16 horses = 4 oxen 6 oxen = 4 elephants 10 elephants = rs . 150000 p = rs . [ ( 24 * 4 * 4 * 150000 ) / ( 10 * 16 * 6 * 10 ) ] p = rs . ( 57600000 / 9600 ) = > p = rs . 6000 answer : d"
Answer: d
Question (gain): a candidate got 31 % of the votes polled and he lost to his rival by 2451 votes . how many votes were cast ?
Options: a ) 6150 , b ) 6250 , c ) 6350 , d ) 6450 , e ) 6550
Rationale: "let x be the total number of votes . 0.31 x + 2451 = 0.69 x 0.38 x = 2451 x = 2451 / 0.38 = 6450 the answer is d ."
Answer: d
Question (gain): find the simple interest on $ 2000 for 3 years at 10 % per annum ?
Options: a ) $ 250 , b ) $ 300 , c ) $ 500 , d ) $ 600 , e ) $ 1000
Rationale: "si = ptr / 100 = 2000 * 3 * 10 / 100 = $ 600 answer is d"
Answer: d
Question (gain): an inspector rejects 10 % of the meters as defective . how many will he examine to reject 10 ?
Options: a ) 100 , b ) 120 , c ) 250 , d ) 200 , e ) 160
Rationale: "then , 10 % of x = 10 ( 10 / 100 ) x = 10 x = ( 10 * 100 * ) / 10 = 100 answer is a"
Answer: a
Question (general): the difference between the place value and the face value of 4 in the numeral 854973 is
Options: a ) 973 , b ) 6973 , c ) 3996 , d ) 6084 , e ) none of these
Rationale: "( place value of 4 ) - ( face value of 4 ) = ( 4000 - 4 ) = 3996 answer : option c"
Answer: c
Question (general): the mean of 50 observations was 36 . it was found later that an observation 29 was wrongly taken as 23 . the corrected new mean is :
Options: a ) 36.1 , b ) 36.5 , c ) 36.22 , d ) 36.12 , e ) 36.18
Rationale: "explanation : correct sum = ( 36 * 50 + 29 - 23 ) = 1806 . correct mean = = 1806 / 50 = 36.12 answer : d ) 36.12"
Answer: d
Question (gain): shawn invested one half of his savings in a bond that paid simple interest for 2 years and received $ 550 as interest . he invested the remaining in a bond that paid compound interest , interest being compounded annually , for the same 2 years at the same rate of interest and received $ 605 as interest . what was the value of his total savings before investing in these two bonds ?
Options: a ) $ 2,750 , b ) $ 5,500 , c ) $ 11,000 , d ) $ 22,000 , e ) $ 44,000
Rationale: "si for 1 st year = 550 / 2 = 275 275 + 275 + si on ( 275 ) = 605 = = > si on 275 = 55 = = > si on 275 = 275 * r * 1 / 100 = 55 r = 20 % now using si for 2 years on t / 2 of the money ( t / 2 ) * 20 * 2 / 100 = 550 t = 550 * 5 = 2750 answer : a"
Answer: a
Question (gain): what percent is 350 gm of 1 kg ?
Options: a ) 25 % , b ) 40 % , c ) 35 % , d ) 8 % , e ) 12 %
Rationale: "1 kg = 1000 gm 350 / 1000 ã — 100 = 35000 / 1000 = 35 % answer is c"
Answer: c
Question (general): 7 people average age is 30 . youngest person age is 3 . find average of the people when youngest was born .
Options: a ) 23 , b ) 24 , c ) 25 , d ) 26 , e ) 27
Rationale: "average age of people = 30 so have total age = 210 before 7 years we have to deduct each person age by seven years 210 - 21 = 189 so average age would be 189 / 7 = 27 answer : e"
Answer: e
Question (general): the average of first five multiples of 8 is :
Options: a ) 3 , b ) 9 , c ) 12 , d ) 15 , e ) 24
Rationale: "solution average = 8 ( 1 + 2 + 3 + 4 + 5 ) / 5 = 120 / 5 = 24 answer e"
Answer: e
Question (general): what is value of ( ( 2 ^ 5 ) * ( 9 ^ 2 ) ) / ( ( 8 ^ 2 ) * ( 3 ^ 5 ) ) = ?
Options: a ) 1 / 6 , b ) 1 / 3 , c ) 2 / 3 , d ) 1 / 4 , e ) 4
Rationale: = > ( ( 2 ^ 5 ) * ( ( 3 ^ 2 ) ^ 2 ) / ( ( 2 ^ 3 ) ^ 2 ) * ( 3 ^ 5 ) ) = > ( ( 2 ^ 5 ) * ( 3 ^ 4 ) ) / ( ( 2 ^ 6 ) * ( 3 ^ 5 ) ) = > 1 / ( 2 * 3 ) = > 1 / 6 option a is answer
Answer: a
Question (geometry): two circular frames are kept one above the other . frame x has a diameter of 16 cm and frame y has a diameter of 12 cm . what fraction of the surface of frame x is not covered by frame y ?
Options: a ) 3 / 5
b ) 7 / 16
c ) 12 / 16
d ) 24 / 12
e ) 2 / 3
Rationale: the questions asks us to find the surface which is not covered by the frame y i . e . , area of the surface not covered . where as circumference is the length along the edge of the circle , 2 * pi * r implies the length of the curve pi * r ^ 2 implies area enclosed by that curve . . hence area of the circle is considered for this problem area of the frame y = pi * r ^ 2 , where r = 6 = > pi * 36 area of the frame x = pi * 64 surface not covered by the frame y = pi * 64 - pi * 36 = pi * 28 fraction of frame x ' s surface is not covered by a frame y = pi * 28 / total area of the frame x = 28 / 64 = 7 / 16 answer is b
Answer: b
Question (physics): a car gets 40 kilometers per gallon of gasoline . how many gallons of gasoline would the car need to travel 140 kilometers ?
Options: a ) 4.5 , b ) 5.5 , c ) 6.5 , d ) 7.5 , e ) 3.5
Rationale: "each 40 kilometers , 1 gallon is needed . we need to know how many 40 kilometers are there in 140 kilometers ? 140 ÷ 40 = 3.5 × 1 gallon = 3.5 gallons correct answer e"
Answer: e
Question (gain): in some quantity of ghee , 60 % of pure ghee and 40 % of is vanaspati . if 10 kg of pure ghee is added , then the strength of vanaspati ghee becomes 20 % . the original quantity was ?
Options: a ) 5 kg , b ) 10 kg , c ) 15 kg , d ) 20 kg , e ) 25 kg
Rationale: let the original quantity be x kg vanaspati ghee in x kg = 40 / 100 * x = 2 x / 5 kg ( 2 x / 5 ) / ( x + 10 ) = 20 / 100 2 x / ( 5 x + 50 ) = 1 / 5 5 x = 50 x = 10 kg answer is b
Answer: b
Question (physics): jack and jill are marathon runners . jack can finish a marathon ( 42 km ) in 6 hours and jill can run a marathon in 4.2 hours . what is the ratio of their average running speed ? ( jack : jill )
Options: a ) 7 / 10 , b ) 15 / 14 , c ) 4 / 5 , d ) 5 / 4 , e ) can not be determined
Rationale: "average speed of jack = distance / time = 42 / 6 = 7 average speed of jill = 42 / ( 4.2 ) = 10 ratio of average speed of jack to jill = 7 / 10 answer a"
Answer: a
Question (general): ( 128.5 x 4 ) + ( 13.8 x 5 ) = ? x 10
Options: a ) 524.48 , b ) 556.02 , c ) 58.3 , d ) 585.64 , e ) 595.46
Rationale: "explanation : ? = ( 128.5 x 4 ) + ( 13.8 x 5 ) / 10 = 514 + 69 / 10 = 58.3 answer : option c"
Answer: c
Question (general): when a natural number n is successively divided by 12 , 34 the remainders are 56 , 78 . what will be the sum of the remainders if the order of the division is reversed ?
Options: a ) 11 , b ) 12 , c ) 10 , d ) 2 , e ) 7
Rationale: 1 2 3 4 5 6 7 8 leave the top right - most number 8 start with bottom right - most number 5 8 * 3 + 7 = 31 31 * 2 + 6 = 68 68 * 1 + 5 = 73 this is the number required now , do the successive division in the reverse order the sum of the remainders is 10 hence , the correct option is c
Answer: c
Question (physics): speed of a boat in still water is 5 km / hr and speed of the stream is 2 kmph . a man rows to a place at a distance of 252 km and comes back to the starting point the total time taken by him is .
Options: a ) 160 hr , b ) 200 hr , c ) 120 hr , d ) 140 hr , e ) 180 hr
Rationale: explanation : speed up stream = 5 - 2 = 3 km / hr speed down stream = 5 + 2 = 7 km / hr total time taken = 252 / 3 + 252 / 7 = 84 + 36 = 120 hr answer : option b
Answer: b
Question (general): each week , harry is paid x dollars per hour for the first 30 hours and 1.5 x dollars for each additional hour worked that week . each week , james is paid x dollars per per hour for the first 40 hours and 2 x dollars for each additional hour worked that week . last week james worked a total of 42 hours if harry and james were paid the same amount last week , how many hours did harry work last week ?
Options: a ) 35 , b ) 36 , c ) 37 , d ) 38 , e ) 39
Rationale: "james worked for 41 hours hence he earned 40 * x + 2 * 2 x = 44 x dollars ; we know that harry also earned the same 44 x dollars , out of which he earned 30 x dollars for thefirst 30 hoursplus 14 x additional dollars . since for each additional hour he gets 1.5 x dollars then he worked for 14 x / 1.5 x = 9 additional hours , so harry worked for total of 30 + 9 = 39 hours . answer : e ."
Answer: e
Question (gain): some of 50 % - intensity red paint is replaced with 25 % solution of red paint such that the new paint intensity is 35 % . what fraction of the original paint was replaced ?
Options: a ) 1 / 35 , b ) 1 / 5 , c ) 2 / 3 , d ) 3 / 5 , e ) 4 / 5
Rationale: "35 % is 10 % - points above 25 % and 15 % - points below 50 % . thus the ratio of 25 % - solution to 50 % - solution is 3 : 2 . 3 / 5 of the original paint was replaced . the answer is d ."
Answer: d
Question (general): the shopkeeper increased the price of a product by 25 % so that customer finds it difficult to purchase the required amount . but somehow the customer managed to purchase only 64 % of the required amount . what is the net difference in the expenditure on that product ?
Options: a ) 12.5 % , b ) 13 % , c ) 15 % , d ) 17 % , e ) 20 %
Rationale: "quantity x rate = price 1 x 1 = 1 0.64 x 1.25 = 0.8 decrease in price = ( 0.2 / 1 ) × 100 = 20 % e )"
Answer: e
Question (physics): an engineer undertakes a project to build a road 10 km long in 30 days and employs 30 men for the purpose . after 10 days , he finds only 2 km of the road has been completed . find the ( approximate ) number of extra men he must employ to finish the work in time .
Options: a ) 30 , b ) 40 , c ) 50 , d ) 60 , e ) 70
Rationale: "30 workers working already let x be the total men required to finish the task in next 20 days 2 km done hence remaining is 8 km also , work has to be completed in next 20 days ( 30 - 10 = 20 ) we know that , proportion of men to distance is direct proportion and , proportion of men to days is inverse proportion hence , x = ( 30 * 8 * 10 ) / ( 2 * 20 ) thus , x = 60 thus , more men needed to finish the task = 60 - 30 = 30 answer : a"
Answer: a
Question (geometry): the number 155 can be written as the sum of the squares of 3 different positive integers . what is the sum of these 3 integers ?
Options: a ) 17 , b ) 16 , c ) 15 , d ) 14 , e ) 21
Rationale: "7 ^ 2 + 5 ^ 2 + 9 ^ 2 = 49 + 25 + 81 = 155 7 + 5 + 9 = 21 hence answer is e"
Answer: e