Cheukting/mathqa huggingface dataset:
Question (general): how many multiples of 10 are there between 10 and 290 ?
Options: a ) 8 , b ) 18 , c ) 27 , d ) 51 , e ) 60
Rationale: "it should be mentioned whether 10 and 290 are inclusive . if 10 and 290 are inclusive , then the answer is ( 290 - 10 ) / 10 + 1 = 29 . if 10 and 290 are not inclusive , then the answer is ( 280 - 20 ) / 10 + 1 = 27 . since oa is c , then we have not inclusive case ."
Answer: c
Question (general): what is the remainder when 1041 * 1047 * 1050 * 1053 is divided by 33 ?
Options: a ) 3 , b ) 27 , c ) 30 , d ) 21 , e ) 18
Rationale: "take the remainder from each of 1041 / 33 , 1047 / 33 and so on . . 1044 / 33 gives remainder = 18 1047 / 33 gives remainder = 24 1050 / 33 gives remainder = 27 1053 / 33 gives remainder = 30 the net remainder is the product of above individual remainders . i . e = 18 * 24 * 27 * 30 break them into pairs 18 * 24 / 33 gives remainder 3 and 27 * 30 / 33 gives remainder 18 so 3 * 18 / 33 gives remainder 21 . d"
Answer: d
Question (general): if the average ( arithmetic mean ) of a and b is 110 , and the average of b and c is 170 , what is the value of a − c ?
Options: a ) − 120 , b ) − 100 , c ) 100 , d ) 135 , e ) it can not be determined from the information given
Rationale: "a + b = 220 b + c = 340 a - c = - 120 . imo option a ."
Answer: a
Question (general): line m lies in the xy - plane . the y - intercept of line m is - 2 , and line m passes through the midpoint of the line segment whose endpoints are ( 2 , 8 ) and ( 144 ) . what is the slope of line m ?
Options: a ) - 2 , b ) - 1 , c ) 0 , d ) 1 , e ) 2
Rationale: the midpoint of ( 2,8 ) and ( 14,4 ) is ( 8,6 ) . the slope of a line through ( 0 , - 2 ) and ( 8,6 ) is ( 6 - ( - 2 ) ) / ( 8 - 0 ) = 8 / 8 = 1 the answer is d .
Answer: d
Question (general): the average weight of a , b and c is 60 kg . if the average weight of a and b be 70 kg and that of b and c be 50 kg , then the weight of b is :
Options: a ) 50 kg , b ) 60 kg , c ) 55 kg , d ) 57 kg , e ) 62 kg
Rationale: "explanation let a , b , c represent their respective weights . then , we have : a + b + c = ( 60 x 3 ) = 180 â € ¦ . ( i ) a + b = ( 70 x 2 ) = 140 â € ¦ . ( ii ) b + c = ( 50 x 2 ) = 100 â € ¦ . ( iii ) adding ( ii ) and ( iii ) , we get : a + 2 b + c = 240 â € ¦ . ( iv ) subtracting ( i ) from ( iv ) , we get : b = 60 . b â € ™ s weight = 60 kg . answer b"
Answer: b
Question (physics): length of a rectangular plot is 22 mtr more than its breadth . if the cost of fencin gthe plot at 26.50 per meter is rs . 5300 , what is the length of the plot in mtr ?
Options: a ) 51 m , b ) 61 m , c ) 71 m , d ) 81 m , e ) 91 m
Rationale: "let breadth = x metres . then , length = ( x + 22 ) metres . perimeter = 5300 m = 200 m . 26.50 2 [ ( x + 22 ) + x ] = 200 2 x + 22 = 100 2 x = 78 x = 39 . hence , length = x + 22 = 61 m b"
Answer: b
Question (gain): a reduction of 20 % in the price of oil enables a house wife to obtain 4 kgs more for rs . 600 , what is the reduced price for kg ?
Options: a ) 20 , b ) 40 , c ) 36 , d ) 30 , e ) 35
Rationale: "600 * ( 20 / 100 ) = 120 - - - - 4 ? - - - - 1 = > rs . 30 answer : d"
Answer: d
Question (general): after spending rs . 5000 on rent , rs . 1500 on milk , rs . 4500 on groceries , rs . 2500 on childrens education rs . 2000 on petrol and rs . 2500 on miscellaneous expenses , mr . kishore saved 10 % of his monthly salary . how much did he save in rs . ?
Options: a ) 2160 , b ) 2350 , c ) 2000 , d ) 2300 , e ) none of these
Rationale: "explanation : total exp = 5000 + 1500 + 4500 + 2500 + 2000 + 2500 = 18000 exp in % = 100 - 10 = 90 % , 18000 = 90 % saving = 10 % = 18000 x 10 / 90 = rs . 2000 answer : c"
Answer: c
Question (physics): jim drove 384 miles of a 1200 miles journey . how many more miles does he need to drive to finish his journey ?
Options: a ) 113 miles , b ) 432 miles , c ) 456 miles , d ) 816 miles , e ) 767 miles
Rationale: "the number of miles to drive to finish his journey is given by 1200 - 384 = 816 miles correct answer d"
Answer: d
Question (general): find the product of the local value and absolute value of 4 in 564823
Options: a ) 1600 , b ) 8000 , c ) 16000 , d ) 12000 , e ) 18000
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 x 4 = 16000 answer : option c
Answer: c
Question (gain): the banker â € ™ s gain on a sum due 3 years hence at 10 % per annum is rs . 60 . the banker â € ™ s discount is
Options: a ) rs . 960 , b ) rs . 840 , c ) rs . 1020 , d ) rs . 760 , e ) rs . 260
Rationale: "solution t . d = ( b . g x 100 / r x t ) = rs . ( 60 x 100 / 10 x 3 ) = rs . 200 . b . d = rs ( 200 + 60 ) = rs . 260 . answer e"
Answer: e
Question (general): robert ' s salary was decreased by 70 % and subsequently increased by 70 % . how much percentage does he lose ?
Options: a ) 10 % , b ) 20 % , c ) 25 % , d ) 30 % , e ) 49 %
Rationale: "let original salary be $ 100 salary after decreasing 70 % = 100 - 100 x 70 / 100 = $ 30 salary after increasing 70 % on $ 30 = 30 + 30 x 70 / 100 = $ 51 percentage of loss = 100 - 51 = 49 % answer : e"
Answer: e
Question (physics): a train covers a distance of 54 km in 15 min . if it takes 8 sec to pass a telegraph post , then the length of the train is ?
Options: a ) 470 , b ) 480 , c ) 490 , d ) 500 , e ) 510
Rationale: "speed = ( 54 / 15 * 60 ) km / hr = ( 216 * 5 / 18 ) m / sec = 60 m / sec . length of the train = 60 * 8 = 480 m . answer : option b"
Answer: b
Question (general): the difference between the value of a number increased by 12.5 % and the value of the original number decreased by 25 % is 30 . what is the original number e ?
Options: a ) 60 , b ) 80 , c ) 40 , d ) 120 , e ) 160
Rationale: "( 1 + 1 / 8 ) x - ( 1 - 1 / 4 ) x = 30 ( 9 / 8 ) x - ( 3 / 4 ) x = 30 x = 80 = e answer : b"
Answer: b
Question (general): what is the remainder when you divide 2 ^ 200 - 3 by 7 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: answer is a . this is very similar to the 32 ^ 32 ^ 32 - 3 divided by 7 question .
Answer: a
Question (other): the ratio of three numbers is 2 : 3 : 4 and their sum is 180 . the second number of the three numbers is ?
Options: a ) 24 , b ) 60 , c ) 27 , d ) 29 , e ) 30
Rationale: "2 : 3 : 4 total parts = 9 9 parts - - > 180 1 part - - - - > 20 the second number of the three numbers is = 3 * 20 = 60 answer : b"
Answer: b
Question (other): if ( log 5 5 ) ( log 4 9 ) ( log 3 2 ) is equal to
Options: a ) 1 , b ) 3 / 2 , c ) 2 , d ) 5 , e ) 7
Rationale: solution given expression = log 9 / log 4 × log 2 / log 3 ‹ = › log 3 ² / log 2 ² × log 2 / log 3 = 2 log 3 / 2 log 2 × log 2 / log 3 = 1 . answer a
Answer: a
Question (general): the total marks obtained by a student in mathematics and physics is 32 and his score in chemistry is 20 marks more than that in physics . find the average marks scored in mathamatics and chemistry together .
Options: a ) 40 , b ) 26 , c ) 27 , d ) 28 , e ) 22
Rationale: "let the marks obtained by the student in mathematics , physics and chemistry be m , p and c respectively . given , m + c = 32 and c - p = 20 m + c / 2 = [ ( m + p ) + ( c - p ) ] / 2 = ( 32 + 20 ) / 2 = 26 . answer : b"
Answer: b
Question (general): in the rectangular coordinate system , if the line x = 4 y + 5 passes through points ( m , n ) and ( m + 2 , n + p ) , what is the value of p ?
Options: a ) 3 , b ) 2 , c ) 1 / 2 , d ) 1 / 3 , e ) 1 / 4
Rationale: "x = 4 y + 5 , and thus y = x / 4 - 5 / 4 the slope is 1 / 4 . the slope of a line through points ( m , n ) and ( m + 2 , n + p ) is ( n + p - n ) / ( m + 2 - m ) = p / 2 p / 2 = 1 / 4 and thus p = 1 / 2 the answer is c ."
Answer: c
Question (general): the average weight of 4 students decreases by 8 kg when one of them weighing 96 kg is replaced by a new student . the weight of the student is
Options: a ) 62 kg , b ) 60 kg , c ) 64 kg , d ) 72 kg , e ) none of these
Rationale: explanation : let the weight of student be x kg . given , difference in average weight = 8 kg = > ( 96 - x ) / 4 = 8 = > x = 64 answer : c
Answer: c
Question (physics): if 4 men working 10 hours a day earn rs . 800 per week , then 9 men working 6 hours a day will earn how much per week ?
Options: a ) rs 840 , b ) rs 1320 , c ) rs 1080 , d ) rs 1680 , e ) none of these
Rationale: "explanation : ( men 4 : 9 ) : ( hrs / day 10 : 6 ) : : 800 : x hence 4 * 10 * x = 9 * 6 * 800 or x = 9 * 6 * 800 / 4 * 10 = 1080 answer : c"
Answer: c
Question (geometry): in a rectangular coordinate system , what is the area of a rhombus whose vertices have the coordinates ( 0 , 4.5 ) , ( 8 , 0 ) , ( 0 , - 4.5 ) , ( - 8 , 0 ) ?
Options: a ) 56 , b ) 72 , c ) 112 , d ) 116 , e ) 120
Rationale: "ares of rhombus = 1 / 2 * d 1 * d 2 length of 1 st diagonal = 8 + 8 = 16 length of 2 nd diagonal = 4.5 + 4.5 = 9 area = 1 / 2 * 16 * 9 = 72 b is the answer"
Answer: b
Question (general): a theater box office sold an average ( arithmetic mean ) of 63 tickets per staff member to a particular movie . among the daytime staff , the average number sold per member was 78 , and among the evening staff , the average number sold was 60 . if there are no other employees , what was the ratio of the number of daytime staff members to the number of evening staff members ?
Options: a ) 2 : 3 , b ) 1 : 4 , c ) 1 : 5 , d ) 6 : 11 , e ) 4 : 7
Rationale: deviation from the mean for the daytime staff = 78 - 63 = 15 . deviation from the mean for the evening staff = 63 - 60 = 3 . thus , the ratio of the number of daytime staff members to the number of evening staff members is 3 : 15 = 1 : 5 . the answer is c .
Answer: c
Question (physics): pipe a fills a swimming pool in 4 hours . pipe b empties the pool in 6 hours . if pipe a was opened at 9 : 00 am and pipe b at 10 : 00 am , at what time will the pool be full ?
Options: a ) 19 : 00 , b ) 17 : 00 , c ) 16 : 00 , d ) 18 : 00 , e ) 20 : 00
Rationale: pipe a fills the pool in 4 hrs . 1 hour ' s work : 1 / 4 pipe b empties the pool in 6 hrs . 1 hour ' s work : 1 / 6 together if they work , 1 hour ' s work = 1 / 4 - 1 / 6 = 1 / 12 given : pipe a started at 9 : 00 a . m and pipe b at 10 : 00 a . m pool filled after 1 hour by pipe a : 1 / 4 or 3 / 12 after 10 : 00 a . m pool filled after 1 hour with both the pipes on : 1 / 12 pool filled after 9 hours with both pipes on : 9 / 12 pool filled in 1 hour + pool filled in 9 hours = 3 / 12 + 9 / 12 = 1 therefore , it takes 10 hrs to fill the pool as pipe a started at 9 : 00 a . m , pool is full at 19 : 00 hrs answer : a
Answer: a
Question (physics): a train running at the speed of 100 km / hr crosses a pole in 9 sec . what is the length of the train ?
Options: a ) 298 m , b ) 250 m , c ) 208 m , d ) 988 m , e ) 299 m
Rationale: "speed = 100 * 5 / 18 = 250 / 9 m / sec length of the train = speed * time = 250 / 9 * 9 = 250 m answer : b"
Answer: b
Question (general): an engineer designed a ball so that when it was dropped , it rose with each bounce exactly one - half as high as it had fallen . the engineer dropped the ball from a 16 - meter platform and caught it after it had traveled 45 meters . how many times did the ball bounce ?
Options: a ) 5 , b ) 4 , c ) 7 , d ) 8 , e ) 9
Rationale: "going down = 16 m going up = 8 - - > total = 24 going down = 8 - - > total = 32 going up = 4 - - > total = 36 going down = 4 - - > total = 40 going up = 2 - - > total = 42 going down = 2 - - > total = 44 going up = 1 - - > total = 45 ( caught ) no of bounce = 4 answer : b"
Answer: b
Question (general): average between 2 sets of numbers is closer to the set with more no ' s ?
Options: a ) 70 , b ) 80 , c ) 90 , d ) 92 , e ) 94
Rationale: "if on a test three people answered 90 % of the questions correctly and two people answered 80 % correctly , then the average for the group is not 85 % but rather 3 × 90 + 2 × 805 = 4305 = 86.3 × 90 + 2 × 805 = 4305 = 86 . here , 90 has a weight of 3 = > it occurs 3 times . whereas 80 has a weight of 2 = > it occurs 2 times . so the average is closer to 90 than to 80 as we have just calculated . b"
Answer: b
Question (gain): a merchant marks his goods up by 30 % and then offers a discount of 10 % on the marked price . what % profit does the merchant make after the discount ?
Options: a ) 17 % , b ) 25 % , c ) 69 % , d ) 31 % , e ) 19 %
Rationale: "let the price be 100 . the price becomes 130 after a 30 % markup . now a discount of 10 % on 130 . profit = 117 - 100 17 % answer a"
Answer: a
Question (general): elvin ' s monthly telephone bill is the sum of the charge for the calls he made during the month and a fixed monthly charge for internet service . elvin ' s total telephone bill for january was $ 46 and elvin ' s total telephone bill for february was 76 $ . if elvin ' s charge for the calls he made in february was twice the charge for the calls he made in january , what is elvin ' s fixed monthly charge for internet service ?
Options: a ) $ 5 , b ) $ 10 , c ) $ 14 , d ) $ 16 , e ) $ 28
Rationale: "bill = fixed charge + charge of calls made in jan , bill = fixed charge ( let , y ) + charge of calls made in jan ( let , x ) = $ 46 in feb , bill = fixed charge ( let , y ) + charge of calls made in feb ( then , 2 x ) = $ 76 i . e . x + y = 46 and 2 x + y = 76 take the difference if two equations i . e . ( 2 x + y ) - ( x + y ) = 76 - 46 i . e . x = 30 i . e . fixed monthly charge , y = 16 answer : option d"
Answer: d
Question (physics): maxwell leaves his home and walks toward brad ' s house at the same time that brad leaves his home and runs toward maxwell ' s house . if the distance between their homes is 70 kilometers , maxwell ' s walking speed is 4 km / h , and brad ' s running speed is 6 km / h , what is the distance traveled by brad ?
Options: a ) 42 , b ) 18 , c ) 20 , d ) 24 , e ) 30
Rationale: "time taken = total distance / relative speed total distance = 70 kms relative speed ( opposite side ) ( as they are moving towards each other speed would be added ) = 6 + 4 = 10 kms / hr time taken = 70 / 10 = 7 hrs distance traveled by brad = brad ' s speed * time taken = 6 * 7 = 42 kms . . . answer - a"
Answer: a
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 18 days , then c alone can do it in ?
Options: a ) 7 days , b ) 3 days , c ) 9 days , d ) 8 days , e ) 2 days
Rationale: "c 9 days c = 1 / 4 - 1 / 12 – 1 / 18 = 1 / 9 = > 9 days"
Answer: c
Question (gain): machine a and machine b are each used to manufacture 440 sprockets . it takes machine a 10 hours longer to produce 440 sprockets than machine b . machine b produces 10 % more sprockets per hour than machine a . how many sprockets per hour does machineaproduce ?
Options: a ) 6 , b ) 6.6 , c ) 60 , d ) 4.4 , e ) 110
Rationale: "time taken by b = t time taken by a = t + 10 qty produced by a = q qty produced by b = 1.1 q for b : t ( 1.1 q ) = 440 qt = 400 for a : ( t + 10 ) ( q ) = 440 qt + 10 q = 440 400 + 10 q = 440 q = 4 so a can produce 4 / hour . then b can produce = 4 ( 1.1 ) = 4.4 / hour . d"
Answer: d
Question (gain): on a certain day , tim invested $ 600 at 10 percent annual interest , compounded annually , and lana invested 800 at 5 percent annual interest , compounded annually . the total amount of interest earned by tim ’ s investment in the first 2 years was how much greater than the total amount of interest earned by lana ’ s investment in the first 2 years ?
Options: a ) $ 5 , b ) $ 15 , c ) $ 44 , d ) $ 100 , e ) $ 105
Rationale: compounded annually means that the interest is applied once per year . one can have 10 % annual interest compounded monthly - in this case 10 % / 12 would be applied each month , or 10 % annual interest compounded daily etc . with respect to the problem at hand , at the end of two years , tim would have 600 ( 1.10 ) ^ 2 = 600 ( 1.21 ) = 726 and lana would have 800 ( 1.05 ) ^ 2 = 800 ( 1.1025 ) = 882 thus , tim earned 126 dollars , while lana earned 82 dollars the difference is $ 44 and the answer is c .
Answer: c
Question (geometry): if y is the smallest positive integer such that 630 multiplied by y is the square of an integer , then y must be
Options: a ) 20 , b ) 50 , c ) 60 , d ) 70 , e ) 140
Rationale: "630 = 2 * 3 ^ 2 * 5 * 7 to be perfect square , we need to multiply by at least 2 * 5 * 7 = 70 . the answer is d ."
Answer: d
Question (physics): today mary ’ s father is 4 times as old as mary . 3 years ago , he was 5 times as old . how old is mary today ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14
Rationale: dad ' s age = 4 m 5 * ( m - 3 ) = 4 m - 3 m = 12 the answer is d .
Answer: d
Question (geometry): a horse is tethered to one corner of a rectangular grassy field 42 m by 26 m with a rope 16 m long . over how much area of the field can it graze ?
Options: a ) 154 cm 2 , b ) 308 m 2 , c ) 201 m 2 , d ) 205 m 2 , e ) none of these
Rationale: "area of the shaded portion = 1 ⁄ 4 × π × ( 16 ) 2 = 201 m 2 answer c"
Answer: c
Question (general): in the xy - coordinate system , if ( m , n ) and ( m + 2 , n + k ) are two points on the line perpendicular to x = 2 y + 5 , then k = ?
Options: a ) - 5 , b ) - 8 , c ) 2 , d ) - 4 , e ) 1
Rationale: "the slope = k / 2 the line perpendicular to x = 2 y + 5 or y = 1 / 2 x - 5 / 2 has a slope = - 1 / ( 1 / 2 ) = - 2 - - - > k / 2 = - 2 - - > k = - 4 answer is d"
Answer: d
Question (general): a batsman in his 17 th innings makes a score of 85 and their by increasing his average by 3 . what is his average after the 17 thinnings ?
Options: a ) 22 , b ) 77 , c ) 26 , d ) 37 , e ) 88
Rationale: "16 x + 85 = 17 ( x + 3 ) x = 34 + 3 = 37 answer : d"
Answer: d
Question (general): the average ( arithmetic mean ) of 4 different integers is 76 . if the largest integer is 90 , what is the least possible value of the smallest integer ?
Options: a ) 1 , b ) 19 , c ) 29 , d ) 30 , e ) 37
Rationale: "total of integers = 76 * 4 = 3004 lowest of the least possible integer is when the middle 2 intergers are at the maximum or equal to the highest possible integer . but all integers are distinct . so if the largest integer is 90 , then the middle 2 will be 88 and 89 lowest of least possible integer = 304 - ( 90 + 89 + 88 ) = 304 - 267 = 37 answer : e"
Answer: e
Question (general): a certain elevator has a safe weight limit of 2,000 pounds . what is the greatest possible number of people who can safely ride on the elevator at one time with the average ( arithmetic mean ) weight of half the riders being 200 pounds and the average weight of the others being 230 pounds ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: lets assume there are 2 x people . half of them have average weight of 200 and other half has 230 . maximum weight is = 2000 so 200 * x + 230 * x = 2000 = > 430 x = 2000 = > x is approximately equal to 5 . so total people is 2 * 5 = 10 we are not taking 10 as answer because say 10 th person has minimum of 200 weight then 200 * 5 + 230 * 5 = 2150 ( which is more than 2000 ) answer c .
Answer: c
Question (general): the average salary of all the workers in a workshop is $ 8000 . the average salary of 7 technicians is $ 12000 and the average salary of the rest is $ 6000 . the total number of workers in the shop is ?
Options: a ) 15 , b ) 18 , c ) 21 , d ) 25 , e ) 31
Rationale: let the total number of workers be x 8000 x = 12000 * 7 + 6000 ( x - 7 ) x = 21 answer is c
Answer: c
Question (geometry): a farmer grows broccoli in his farm that is in the shape of a square . each broccoli takes 1 square foot of area in his garden . this year , he has increased his output by 101 broccoli when compared to last year . the shape of the area used for growing the broccoli has remained a square in both these years . how many broccoli did he produce this year ?
Options: a ) 2400
b ) 2601
c ) 1987
d ) 2000
e ) can not be determined
Rationale: explanatory answer the shape of the area used for growing broccoli has remained a square in both the years . let the side of the square area used for growing broccoli this year be x ft . therefore , the area of the ground used for cultivation this year = x 2 sq . ft . let the side of the square area used for growing broccoli last year be y ft . therefore , the area of the ground used for cultivation last year = y 2 sq . ft . as the number of broccoli grown has increased by 101 , the area would have increased by 101 sq ft because each broccoli takes 1 sq ft space . hence , x 2 - y 2 = 101 ( x + y ) ( x - y ) = 101 . 101 is a prime number and hence it will have only two factors . i . e . , 101 and 1 . therefore , 101 can be expressed as product of 2 numbers in only way = 101 * 1 i . e . , ( x + y ) ( x - y ) = 101 * 1 so , ( x + y ) should be 101 and ( x - y ) should be 1 . solving the two equations we get x = 51 and y = 50 . therefore , number of broccoli produced this year = x 2 = 512 = 2601 . alternative approach : use answer choices the area in both the years are squares of two numbers . that rules out choice a , c and d . as 2400,1987 and 2000 are not the square of any number . check choice b : if this year ' s produce is 2601 , last year ' s produce would have been 2601 - 101 = 2500 2500 is the square of 50 . so , 2601 is the answer . choice b
Answer: b
Question (physics): two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds . the ratio of their speeds i
Options: a ) 1 : 3 , b ) 3 : 2 , c ) 3 : 4 , d ) 4 : 2 , e ) none of these
Rationale: "explanation : let the speeds of the two trains be x m / sec and y m / sec respectively . then , length of the first train = 27 x metres , and length of the second train = 17 y metres . 27 x + 17 y / x + y = 23 27 x + 17 y = 23 x + 23 y 4 x = 6 y x / y = 3 / 2 answer is b"
Answer: b
Question (physics): a person can swim in still water at 10 km / h . if the speed of water 8 km / h , how many hours will the man take to swim back against the current for 16 km ?
Options: a ) 3 , b ) 7 , c ) 5 , d ) 8 , e ) 6
Rationale: "m = 10 s = 8 us = 10 - 8 = 2 d = 16 t = 16 / 2 = 8 answer : d"
Answer: d
Question (gain): 90 students represent x percent of the boys at jones elementary school . if the boys at jones elementary make up 60 % of the total school population of x students , what is x ?
Options: a ) 122 , b ) 150 , c ) 225 , d ) 250 , e ) 500
Rationale: "90 = x / 100 * 60 / 100 * x = > x ^ 2 = 9 * 10000 / 6 = > x = 122 a"
Answer: a
Question (physics): maxwell leaves his home and walks toward brad ' s house at the same time that brad leaves his home and runs toward maxwell ' s house . if the distance between their homes is 65 kilometers , maxwell ' s walking speed is 2 km / h , and brad ' s running speed is 3 km / h . what is the distance traveled by maxwell when they meet in the middle ?
Options: a ) 25 , b ) 23 , c ) 22 , d ) 24 , e ) 26
Rationale: "consider max starts from point a and brad starts from point b and move towards each other . assume they shall meet at point o after time ' t ' . the question asks us to find oa . from the question stem we can make out : - distance oa = 50 km - distance ob = > 2 xt = 65 - 3 xt ( i . e distance = speed x time ) = > 5 t = 65 hence t = 13 oa = 2 x 13 = 26 km answer : e"
Answer: e
Question (general): what is the smallest integer that is multiple of 5 , 7,9
Options: a ) a ) 70 , b ) b ) 315 , c ) c ) 200 , d ) d ) 280 , e ) e ) 140
Rationale: "it is the lcm of 5 , 7 and 9 which is 315 . the answer is b ."
Answer: b
Question (probability): the odds in favour of an events are 3 : 5 . the probability of occurrence of the event is
Options: a ) 3 / 8 , b ) 2 / 7 , c ) 1 / 3 , d ) 2 / 5 , e ) 6 / 7
Rationale: number of cases favourable to e = 3 total number of cases = 3 + 5 = 8 p ( e ) = 3 / 8 answer is a
Answer: a