Cheukting/mathqa huggingface dataset:
Question (physics): two good train each 500 m long , are running in opposite directions on parallel tracks . their speeds are 45 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 ) 48 sec , d ) 60 sec , e ) none
Rationale: sol . relative speed = ( 45 + 30 ) km / hr = ( 75 x 5 / 18 ) m / sec = ( 125 / 6 ) m / sec . distance covered = ( 500 + 500 ) m = 1000 m . required time = ( 1000 x 6 / 125 ) sec = 48 sec . answer c
Answer: c
Question (general): in a tree , 2 / 5 of the birds are robins while the rest are bluejays . if 1 / 3 of the robins are female and 2 / 3 of the bluejays are female , what fraction of the birds in the tree are male ?
Options: a ) 3 / 5 , b ) 4 / 15 , c ) 7 / 15 , d ) 8 / 15 , e ) 17 / 30
Rationale: the fraction of birds that are male robins is ( 2 / 3 ) ( 2 / 5 ) = 4 / 15 . the fraction of birds that are male bluejays is ( 1 / 3 ) ( 3 / 5 ) = 1 / 5 . the total fraction of male birds is 4 / 15 + 1 / 5 = 7 / 15 . the answer is c .
Answer: c
Question (physics): what distance will be covered by a bus moving at 90 kmph in 20 seconds ?
Options: a ) 500 , b ) 600 , c ) 289 , d ) 276 , e ) 207
Rationale: "90 kmph = 90 * 5 / 18 = 25 mps d = speed * time = 25 * 20 = 500 m . answer : a"
Answer: a
Question (physics): in traveling from a dormitory to a certain city , a student went 1 / 2 of the way by foot , 1 / 4 of the way by bus , and the remaining 6 kilometers by car . what is the distance , in kilometers , from the dormitory to the city ?
Options: a ) 35 , b ) 24 , c ) 14 , d ) 24 , e ) 12
Rationale: "whole trip = distance by foot + distance by bus + distance by car x = 1 / 2 x + 1 / 4 x + 6 x - 1 / 2 x - 1 / 4 x = 6 x = 24 km option : d"
Answer: d
Question (physics): the speed of a car is 80 km in the first hour and 60 km in the second hour . what is the average speed of the car ?
Options: a ) 76 kmph , b ) 70 kmph , c ) 87 kmph , d ) 56 kmph , e ) 86 kmph
Rationale: "s = ( 80 + 60 ) / 2 = 70 kmph answer : b"
Answer: b
Question (gain): if a town of 15,000 people is growing at a rate of approx . 1 % per year , the population of the town in 5 years will be closest to ?
Options: a ) a . 16000 , b ) b . 17000 , c ) c . 18000 , d ) d . 19000 , e ) e . 20000
Rationale: 1 % is quite small and hence the answer is a )
Answer: a
Question (other): the ratio , by volume , of bleach ( b ) to detergent ( d ) to water in a certain solution is 2 : 40 : 100 . the solution will be altered so that the ratio of bleach to detergent is tripled while the ratio of detergent to water is halved . if the altered solution will contain 300 liters of water , how many liters of detergent will it contain ?
Options: a ) 60
b ) 50
c ) 40
d ) 80
e ) 70
Rationale: b : d : w = 2 : 40 : 100 bnew / dnew = ( 1 / 3 ) * ( 2 / 40 ) = ( 1 / 60 ) dnew / wnew = ( 1 / 2 ) * ( 40 / 100 ) = ( 1 / 5 ) wnew = 300 dnew = wnew / 5 = 300 / 5 = 60 so , answer will be a
Answer: a
Question (physics): when 0.232323 . . . . . is converted into a fraction , then the result is
Options: a ) 23 / 99 , b ) 2 / 9 , c ) 1 / 5 , d ) 23 / 100 , e ) 23 / 98
Rationale: 0.232323 . . . = 0.23 = 23 / 99 answer is a .
Answer: a
Question (physics): in a garden , 26 trees are planted at equal distances along a yard 400 metres long , one tree being at each end of the yard . what is the distance between two consecutive trees ?
Options: a ) 10 , b ) 8 , c ) 12 , d ) 14 , e ) 16
Rationale: 26 trees have 25 gaps between them . length of each gap = 400 / 25 = 16 i . e . , distance between two consecutive trees = 16 answer is e .
Answer: e
Question (physics): 36 men can complete a piece of work in 18 days . in how many days will 108 men complete the same work ?
Options: a ) 24 , b ) 77 , c ) 6 , d ) 29 , e ) 21
Rationale: "explanation : less men , means more days { indirect proportion } let the number of days be x then , 108 : 36 : : 18 : x x = 6 answer : c ) 6 days"
Answer: c
Question (geometry): the length and breadth of a rectangle is increased by 11 % and 22 % respectively . what is the increase in the area ?
Options: a ) 35.22 , b ) 33.52 , c ) 35.42 , d ) 36.22 , e ) 38.42
Rationale: "100 * 100 = 10000 111 * 122 = 13542 - - - - - - - - - - - - 3542 10000 - - - - - - - 3542 100 - - - - - - - - - - 35.42 answer c"
Answer: c
Question (general): the simple interest on a sum of money will be rs . 700 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 ) 2261 , b ) 2888 , c ) 1400 , d ) 2699 , e ) 2771
Rationale: "p - - - 10 - - - - 700 p - - - 5 - - - - - 350 3 p - - - 5 - - - - - 1050 - - - - - - = > 1400 answer : c"
Answer: c
Question (general): barbata invests $ 2000 in the national bank at 5 % . how much additional money must she invest at 8 % so that the total annual income will be equal to 6 % of her entire investment ?
Options: a ) 1200 , b ) 3000 , c ) 1000 , d ) 3600 , e ) 2400
Rationale: "let the additional invested amount for 8 % interest be x ; equation will be ; 2000 + 0.05 * 2000 + x + 0.08 x = 2000 + x + 0.06 ( 2000 + x ) 0.05 * 2000 + 0.08 x = 0.06 x + 0.06 * 2000 0.02 x = 2000 ( 0.06 - 0.05 ) x = 2000 * 0.01 / 0.02 = 1000 ans : ` ` c ' '"
Answer: c
Question (general): what is the greatest positive integer x such that 5 ^ x is a factor of 125 ^ 10 ?
Options: a ) 5 , b ) 9 , c ) 10 , d ) 20 , e ) 30
Rationale: "125 ^ 10 = ( 5 ^ 3 ) ^ 10 = 5 ^ 30 answer : e"
Answer: e
Question (gain): a dishonest milkman wants to make a profit on the selling of milk . he would like to mix water ( costing nothing ) with milk costing rs . 35 per litre so as to make a profit of 20 % on cost when he sells the resulting milk and water mixture for rs . 40 in what ratio should he mix the water and milk ?
Options: a ) 1 : 20 , b ) 1 : 10 , c ) 1 : 8 , d ) 1 : 4 , e ) 6 : 11
Rationale: "water = w ( liter ) milk = m ( liter ) = = > cost = price x quantity = 0.35 m = = > revenue = price x quantity = 0.40 ( m + w ) = = > profit = 0.40 ( m + w ) - 0.35 m = 0.2 * ( 0.35 m ) [ 20 % of cost ] = = > 0.40 m + 0.40 w - 0.35 m = 0.07 m = = > 0.02 m = 0.40 w = = > m / w = 0.40 / 0.02 = 20 - - or - - w / m = 1 / 20 a is correct ."
Answer: a
Question (physics): two trains start simultaneously from opposite ends of a 150 - km route and travel toward each other on parallel tracks . train x , traveling at a constant rate , completes the 150 - km trip in 4 hours . train y , travelling at a constant rate , completes the 150 - km trip in 3.5 hours . how many kilometers had train x traveled when it met train y ?
Options: a ) 68 , b ) 70 , c ) 72 , d ) 74 , e ) 76
Rationale: if the two trains cover a total distance d , then train x travels ( 7 / 15 ) * d while train y travels ( 8 / 15 ) * d . if the trains travel 150 km to the meeting point , then train x travels ( 7 / 15 ) * 150 = 70 km . the answer is b .
Answer: b
Question (general): ( ( 1 ^ ( m + 1 ) ) / ( 5 ^ ( m + 1 ) ) ) ( ( 1 ^ 18 ) / ( 4 ^ 18 ) ) = 1 / ( 2 ( 10 ) ^ 35 ) what is m ?
Options: a ) 17 , b ) 18 , c ) 34 , d ) 35 , e ) 36
Rationale: ( ( 1 ^ ( m + 1 ) ) / ( 5 ^ ( m + 1 ) ) ) ( ( 1 ^ 18 ) / ( 4 ^ 18 ) ) = 1 / ( 2 ( 10 ) ^ 35 ) ( ( 1 / 5 ) ^ ( m + 1 ) ) * ( ( 1 / 2 ) ^ 36 ) = 1 / ( 2 * ( 2 * 5 ) ^ 35 ) ) 2 ^ 36 will cancel out , since 1 can be written as 1 ^ 35 , so ( 1 / 5 ) ^ ( m + 1 ) = ( 1 / 5 ) ^ 35 ( ( 1 / 5 ) ^ ( m + 1 ) ) * ( ( 1 / 2 ) ^ 36 ) = 1 / [ ( 2 ^ 36 ) * ( 5 ^ 35 ) ] so , m = 34 answer c
Answer: c
Question (general): a student chose a number , multiplied it by 2 , then subtracted 138 from the result and got 106 . what was the number he chose ?
Options: a ) 123 , b ) 267 , c ) 277 , d ) 122 , e ) 120
Rationale: "let xx be the number he chose , then 2 â ‹ … x â ˆ ’ 138 = 106 x = 122 answer : d"
Answer: d
Question (physics): a honey bee flies for 10 seconds , from a daisy to a rose . it immediately continues to a poppy , flying for 6 additional seconds . the distance the bee passed , flying from the daisy to the rose is 18 meters longer than the distance it passed flying from the rose to the poppy . the bee flies to the poppy at 3 meters per second faster than her speed flying to the rose . the bee flies how many meters per second from the daisy to the rose ?
Options: a ) 1.4 , b ) 1.5 , c ) 1.6 , d ) 1.8 , e ) 1.0
Rationale: "let the speed be ' s ' and let the distance between rose and poppy be ' x ' the problem boils down to : rose to poppy : s + 3 = x / 6 - - - - - - - 1 daisy to rose : s = ( x + 18 ) / 10 - - - - - - 2 so from 1 we can re write x as x = 6 s + 18 substitute the value of x in 2 gives us s = 1.8 m / s d"
Answer: d
Question (gain): if the cost price is 98 % of sp then what is the profit %
Options: a ) 4.07 % , b ) 4 % , c ) 2.7 % , d ) 2.04 % , e ) 2.08 %
Rationale: "sol . sp = rs 100 : then cp = rs 98 : profit = rs 2 . profit = { ( 2 / 98 ) * 100 } % = 2.04 % answer is d ."
Answer: d
Question (physics): mary passed a certain gas station on a highway while traveling west at a constant speed of 50 miles per hour . then , 15 minutes later , paul passed the same gas station while traveling west at a constant speed of 60 miles per hour . if both drivers maintained their speeds and both remained on the highway for at least 3 hours , how long after he passed the gas station did paul catch up with mary ?
Options: a ) 1.5 , b ) 1.3 , c ) 1.25 , d ) 1.6 , e ) 2
Rationale: "d = rt m : r = 50 mph , t = t + 1 / 4 hr d = 50 ( t + 1 / 4 ) p : r = 60 , t = t d = 60 t since they went the same distance : 50 t + 50 / 4 = 60 t 10 t = 50 / 4 t = 1.25 or 1 hr , 15 min c"
Answer: c
Question (gain): the banker â € ™ s discount of a certain sum of money is rs . 78 and the true discount on the same sum for the same time is rs . 66 . the sum due is
Options: a ) 429 , b ) 280 , c ) 360 , d ) 450 , e ) none
Rationale: sol . sum = b . d . * t . d . / b . d . - t . d . = rs . [ 78 * 66 / 78 - 66 ] = rs . [ 78 * 66 / 12 ] = rs . 429 answer a
Answer: a
Question (general): right now , al and eliot have bank accounts , and al has more money than eliot . the difference between their two accounts is 1 / 10 of the sum of their two accounts . if al ’ s account were to increase by 10 % and eliot ’ s account were to increase by 20 % , then al would have exactly $ 22 more than eliot in his account . how much money does eliot have in his account right now ?
Options: a ) $ 110 , b ) $ 152.3 , c ) $ 180 , d ) $ 220 , e ) $ 260
Rationale: "lets assume al have amount a in his bank account and eliot ' s bank account got e amount . we can form an equation from the first condition . a - e = 1 / 10 * ( a + e ) = = > 9 a = 11 e - - - - - - - - - - - - ( 1 ) second condition gives two different amounts , al ' s amount = 1.1 a and eliot ' s amount = 1.2 e 1.1 a = 22 + 1.2 e = = > 11 a = 220 + 12 e - - - - - - - ( 2 ) substituting ( 1 ) in ( 2 ) : 11 e / 9 * 11 = 220 + 12 e or ( 121 / 9 - 12 ) e = 220 or 13 / 9 e = 220 e = 220 * 9 / 13 = 152.3 b"
Answer: b
Question (general): a charitable association sold an average of 66 raffle tickets per member . among the female members , the average was 70 raffle tickets . the male to female ratio of the association is 1 : 2 . what was the average number q of tickets sold by the male members of the association
Options: a ) 50 , b ) 56 , c ) 58 , d ) 62 , e ) 66
Rationale: "given that , total average q sold is 66 , male / female = 1 / 2 and female average is 70 . average of male members isx . ( 70 * f + x * m ) / ( m + f ) = 66 - > solving this equation after substituting 2 m = f , x = 58 . ans c ."
Answer: c
Question (general): subtract the absolute value from the local value of 4 in 564823
Options: a ) 196 , b ) 1996 , c ) 2996 , d ) 3996 , e ) 6000
Rationale: explanation : place value = local value face value = absolute value the place value of 4 in 564823 is 4 x 1000 = 4000 the face value of 4 in 564823 is nothing but 4 . = > 4000 - 4 = 3996 answer : option d
Answer: d
Question (gain): machine a and machine g are each used to manufacture 660 sprockets . it takes machine a 10 hours longer to produce 660 sprockets than machine g . machine g produces 10 percent more sprockets per hour than machine a . how many sprockets per hour does machine a produces ?
Options: a ) 6 , b ) 6.6 , c ) 60 , d ) 100 , e ) 110
Rationale: [ reveal ] spoiler : timeg : 660 / x timea : [ 660 / x + 10 ] 660 / x = [ 660 / x + 10 ] * 110 / 100 660 / x = 66 * 11 / x + 10 660 x + 10 = 66 * 11 * x 660 x + 6600 = 66 * 11 * x x = 100 plug in back to timea 660 / 100 + 10 = > 660 / 110 = 6
Answer: a
Question (general): for all positive integers m , [ m ] = 3 m when m is odd and [ m ] = ( 1 / 2 ) * m when m is even . what is [ 7 ] * [ 4 ] equivalent to ?
Options: a ) [ 28 ] , b ) [ 84 ] , c ) [ 42 ] , d ) [ 48 ] , e ) [ 14 ]
Rationale: "[ 7 ] * [ 4 ] = 21 * 2 = 42 = ( 1 / 2 ) ( 84 ) = [ 84 ] the answer is b ."
Answer: b
Question (general): what is the tens digit of 6 ^ 21 ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: "the tens digit of 6 in integer power starting from 2 ( 6 ^ 1 has no tens digit ) repeats in a pattern of 5 : { 3 , 1 , 9 , 7 , 5 } : the tens digit of 6 ^ 2 = 36 is 3 . the tens digit of 6 ^ 3 = 216 is 1 . the tens digit of 6 ^ 4 = . . . 96 is 9 . the tens digit of 6 ^ 5 = . . . 76 is 7 . the tens digit of 6 ^ 6 = . . . 56 is 5 . the tens digit of 6 ^ 7 = . . . 36 is 3 again . etc . . . 21 has the form 5 n + 1 , so the tens digit of 6 ^ 21 is 5 . the answer is c ."
Answer: c
Question (general): machine x and machine b are each used to manufacture 660 sprockets . it takes machine x 10 hours longer to produce 660 sprockets than machine b . machine b produces 10 percent more sprockets per hour than machine x . how many sprockets per hour does machine x produces ?
Options: a ) 6 , b ) 6.6 , c ) 60 , d ) 100 , e ) 110
Rationale: i think the correct answer is a . machine x produces at a speed of x sp / hour and b at a speed of b sp / hour . so , 660 / x = ( 660 / b ) + 10 and x = 1,1 x - - - > 1,1 * 660 = 660 + 11 x - - - > a = 6 , so answer a is correct
Answer: a
Question (physics): a can do a piece of work in 2 hours ; b and c together can do it in 3 hours , while a and c together can do it in 2 hours . how long will b alone take to do it ?
Options: a ) 12 , b ) 9 , c ) 8 , d ) 6 , e ) 3
Rationale: "a ' s 1 hour ' s work = 1 / 2 ; ( b + c ) ' s 1 hour ' s work = 1 / 3 ; ( a + c ) ' s 1 hour ' s work = 1 / 2 . ( a + b + c ) ' s 1 hour ' s work = ( 1 / 2 + 1 / 3 ) = 5 / 6 . b ' s 1 hour ' s work = ( 5 / 6 - 1 / 2 ) = 1 / 3 . therefore a alone will take 3 hours to do the work . e"
Answer: e
Question (general): the ages of two persons differ by 16 years . 6 years ago , the elder one was 3 times as old as the younger one . what are their present ages of the elder person
Options: a ) 11 , b ) 66 , c ) 28 , d ) 30 , e ) 99
Rationale: "let ' s take the present age of the elder person = x and the present age of the younger person = x – 16 ( x – 6 ) = 3 ( x - 16 - 6 ) = > x – 6 = 3 x – 66 = > 2 x = 60 = > x = 60 / 2 = 30 answer : d"
Answer: d
Question (gain): in one alloy there is 12 % chromium while in another alloy it is 8 % . 10 kg of the first alloy was melted together with 30 kg of the second one to form a third alloy . find the percentage of chromium in the new alloy .
Options: a ) 9.4 % , b ) 9.6 % , c ) 9 % , d ) 9.8 % , e ) 10 %
Rationale: "the amount of chromium in the new 10 + 30 = 40 kg alloy is 0.12 * 10 + 0.08 * 30 = 3.6 kg , so the percentage is 3.6 / 40 * 100 = 9 % . answer : c"
Answer: c
Question (physics): an automotive test consisted of driving a car the same distance 3 separate times , first at an average rate of 4 miles per hour , then 5 miles per hour , then 6 miles per hour . if the test took 37 hours to complete , how many miles was the car driven during the entire test ?
Options: a ) 100 , b ) 120 , c ) 180 , d ) 200 , e ) 240
Rationale: x is the segment to be traveled x / 4 + x / 5 + x / 6 = 37 or 74 x / 120 = 37 x = 60 miles . total distance = 3 * 60 = 180 miles c
Answer: c
Question (physics): a can do a work in 12 days . b can do the same work in 24 days . if both a & b are working together in how many days they will finish the work ?
Options: a ) 3 , b ) 5 , c ) 8 , d ) 2 , e ) 6
Rationale: "a rate = 1 / 12 b rate = 1 / 24 ( a + b ) rate = ( 1 / 12 ) + ( 1 / 24 ) = 1 / 8 a & b finish the work in 8 days correct option is c"
Answer: c
Question (gain): a , b and c invests rs . 2000 , rs . 3000 and rs . 4000 in a business . after 2 year a removed his money ; b and c continued the business for two more year . if the net profit after 3 years be rs . 4000 , then a ' s share in the profit is ?
Options: a ) 460 , b ) 289 , c ) 220 , d ) 400 , e ) 640
Rationale: "2 * 24 : 3 * 36 : 4 * 36 4 : 9 : 12 4 / 25 * 4000 = 640 answer : e"
Answer: e
Question (general): balls of equal size are arranged in rows to form an equilateral triangle . the top most row consists of one ball , the 2 nd row of two balls and so on . if 19 balls are added , then all the balls can be arranged in the shape of square and each of the sides of the square contain 8 balls less than the each side of the triangle did . how many balls made up the triangle ?
Options: a ) 465 , b ) 2209 , c ) 2878 , d ) 1210 , e ) 1560
Rationale: "as expected , this question boils down to 2 equation , consider total number of balls in triangle = t and number of balls in last row = x . 1 + 2 + 3 + . . . + x = t x ( x + 1 ) / 2 = t - - - - ( a ) as mentioned in the question , side of a square will be ( x - 8 ) and total number of balls in square will be ( t + 19 ) ( x - 8 ) ^ 2 = t + 19 - - - - - ( b ) now the hardest part of the question will be to solve these 2 equations and this looks like time consuming but the easy way will be plug and play . also , we ' ve to find a value of t ( from 5 optiosn given below ) which can make a square of a a number . one we know this , it will be a cake walk . we can see that option a fits this criteria in eq ( b ) . add - 465 + 19 = 484 = 22 ^ 2 = ( x - 8 ) ^ 2 hence , x = 30 cross check by putting in eq ( a ) = x ( x + 1 ) / 2 = t = > 30 * 31 / 2 = 465 hence , answer is a ."
Answer: a
Question (general): the average of 5 quantities is 10 . the average of 3 of them is 4 . what is the average of remaining 2 numbers ?
Options: a ) 19 , b ) 14 , c ) 8 , d ) 9.5 , e ) none of these
Rationale: answer : a ( 5 x 10 - 3 x 4 ) / 2 = 19
Answer: a
Question (physics): a tank is 25 m long 12 m wide and 6 m deep . the cost of plastering its walls and bottom at 70 paise per sq m is
Options: a ) rs . 258.80 , b ) rs . 358.80 , c ) rs . 458.80 , d ) rs . 520.80 , e ) none of these
Rationale: "explanation : area to be plastered = [ 2 ( l + b ) ã — h ] + ( l ã — b ) = [ 2 ( 25 + 12 ) ã — 6 ] + ( 25 ã — 12 ) = 744 sq m cost of plastering = 744 ã — ( 70 / 100 ) = rs . 520.80 answer : d"
Answer: d
Question (other): how many odd factors does 520 have ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 8
Rationale: "start with the prime factorization : 520 = 2 * 5 * 13 for odd factors , we put aside the factor of two , and look at the other prime factors . set of exponents = { 1 , 1 } plus 1 to each = { 2 , 2 } product = 2 * 2 = 4 therefore , there are 4 odd factors of 520 . answer : b ."
Answer: b
Question (general): if the sum of two numbers is 22 and the sum of their squares is 460 , then the product of the numbers is
Options: a ) 40 , b ) 44 , c ) 12 , d ) 88 , e ) 48
Rationale: "according to the given conditions x + y = 22 and x ^ 2 + y ^ 2 = 460 now ( x + y ) ^ 2 = x ^ 2 + y ^ 2 + 2 xy so 22 ^ 2 = 460 + 2 xy so xy = 24 / 2 = 12 answer : c"
Answer: c
Question (general): what is the value of n if the sum of the consecutive odd integers from 1 to n equals 169 ?
Options: a ) 47 , b ) 25 , c ) 37 , d ) 33 , e ) 29
Rationale: # of terms = ( n - 1 / 2 ) + 1 { ( last term - first term ) / 2 + 1 | sum = ( 1 + n ) / 2 * # of terms = ( n + 1 ) ^ 2 / 4 = 169 n + 1 = 13 * 2 n + 1 = 26 n = 25 . answer : b
Answer: b
Question (general): the total number of plums that grew during each year on a certain plum tree was equal to the number of plums that grew during the previous year , less the age of the tree in years ( rounded to the nearest lower integer . ) during its 3 rd year , this plum tree grew 50 plums . how many plums did it grow during its 6 th year ?
Options: a ) a ) 41 , b ) b ) 38 , c ) c ) 35 , d ) d ) 29 , e ) e ) 28
Rationale: the answer shud be 38 . ( 50 - 3 - 4 - 5 = 38 ) yes , if you go the 50 - 3 way , then it will be 38 . if instead you go the 50 - 4 way ( which they have suggested ) , the answer will be 35 . as i said , there is ambiguity here . answer is c
Answer: c
Question (physics): a can finish a work in 8 days and b can do same work in half the time taken by a . then working together , what part of same work they can finish in a day ?
Options: a ) 3 / 5 , b ) 3 / 6 , c ) 3 / 7 , d ) 3 / 8 , e ) none of these
Rationale: "explanation : please note in this question , we need to answer part of work for a day rather than complete work . it was worth mentioning here because many do mistake at this point in hurry to solve the question so lets solve now , a ' s 1 day work = 1 / 8 b ' s 1 day work = 1 / 4 [ because b take half the time than a ] ( a + b ) ' s one day work = ( 1 / 8 + 1 / 4 ) = 3 / 8 so in one day 3 / 8 work will be done answer : d"
Answer: d
Question (physics): donovan and michael are racing around a circular 500 - meter track . if donovan runs each lap in 45 seconds and michael runs each lap in 40 seconds , how many laps will michael have to complete in order to pass donovan , assuming they start at the same time ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13
Rationale: "one way of approaching this question is by relative speed method 1 . speed / rate of donovan = distance / time = > 500 / 45 = > 100 / 9 2 . speed / rate of michael = distance / time = > 500 / 40 = > 50 / 4 relative speed between them = 50 / 4 - 100 / 9 = > 25 / 36 ( we subtract the rates if moving in the same direction and add the rates if moving in the opposite direction ) in order to pass donovan - distance to be covered = 500 , relative rate = 50 / 36 total time taken by micheal to surpass donovan = distance / rate = > 500 * 36 / 50 = > 3600 / 10 = > 360 no . of laps taken by michael = total time / michael ' s rate = > 360 / 40 = > 9 hence correct answer is 9 laps . a"
Answer: a
Question (physics): if m = | | n – 3 | – 2 | , for how many values of n is m = 6 ?
Options: a ) 1 , b ) 3 , c ) 4 , d ) 5 , e ) 2
Rationale: "m = | | n – 3 | – 2 | can be 4 only and only when n - 3 = + / - 8 . so there are 2 values of n answer : e"
Answer: e
Question (gain): in order to obtain an income of rs . 650 from 10 % stock at rs . 96 , one must make an investment of :
Options: a ) 3488 , b ) 6240 , c ) 2776 , d ) 2889 , e ) 7721
Rationale: "explanation : to obtain rs . 10 , investment = rs . 96 . to obtain rs . 650 , investment = = rs . 6240 answer : b ) 6240"
Answer: b
Question (general): in a group of 68 students , each student is registered for at least one of 3 classes – history , math and english . 20 - one students are registered for history , 20 - 6 students are registered for math , and thirty - 4 students are registered for english . if only 3 students are registered for all 3 classes , how many students are registered for exactly two classes ?
Options: a ) 13 , b ) 10 , c ) 9 , d ) 8 , e ) 7
Rationale: a u b u c = a + b + c - ab - bc - ac + abc 68 = 21 + 26 + 34 - ab - bc - ac + 3 = > ab + bc + ac = 16 exactly two classes = ab + bc + ac - 3 abc = 16 - 3 * 3 = 7 hence e
Answer: e