Cheukting/mathqa huggingface dataset:
Question (general): the lowest number which should be added to 1277 so that the sum is exactly divisible by 3 , 2 , 5 , 4 and 7 is :
Options: a ) 303 , b ) 403 , c ) 203 , d ) 453 , e ) 203
Rationale: "l . c . m . of 5 , 6 , 4 and 3 = 420 . on dividing 1277 by 420 , the remainder is 17 . number to be added = ( 420 - 17 ) = 403 . answer : option ' b '"
Answer: b
Question (general): father is aged 3 times more than his son ronit . after 8 years , he would be two and half times if ronit ' s age . after further 8 years , how many times would he be of ronit ' s age ?
Options: a ) 2 times , b ) 2.5 times , c ) 3 times , d ) 3.8 times , e ) 4 times
Rationale: ronit ' s present age be x years . then , father ' s present age = ( x + 3 x ) years = 4 x years therefore ( 4 x + 8 ) = 5 / 2 ( x + 8 ) 8 x + 16 = 5 x + 40 3 x = 24 , x = 8 , ratio = ( 4 x + 16 ) / ( x + 16 ) = 48 / 24 = 2 , correct answer ( a )
Answer: a
Question (physics): due to construction , the speed limit along an 12 - mile section of highway is reduced from 55 miles per hour to 35 miles per hour . approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "12 / 35 - 12 / 55 = 12 / 5 * ( 11 - 7 ) / 77 = 12 / 5 * 4 / 77 * 60 min = 12 * 12 * 4 / 77 = 576 / 77 ~ 7.4 answer - d"
Answer: d
Question (geometry): the area of sector of a circle whose radius is 12 metro and whose angle at the center is 54 â ° is ?
Options: a ) 52.6 , b ) 52.9 , c ) 67.9 , d ) 52.1 , e ) 52.2
Rationale: "54 / 360 * 22 / 7 * 12 * 12 = 67.9 m 2 answer : c"
Answer: c
Question (gain): by selling 10 pens for a rupee a woman loses 18 % . how many for a rupee should he sell in order to gain 30 % ?
Options: a ) 12 , b ) 14 , c ) 45 , d ) 6 , e ) 7
Rationale: "d 82 % - - - 10 130 % - - - ? 82 / 130 * 10 = 6"
Answer: d
Question (general): what is the greatest number of 4 digits which is divisible by 15 , 25 , 40 and 75 ?
Options: a ) 9800 , b ) 9600 , c ) 9400 , d ) 9500 , e ) 9200
Rationale: greatest number of four digits = 9999 lcm of 15 , 25 , 40 and 75 = 600 9999 ÷ 600 = 16 , remainder = 399 hence , greatest number of four digits which is divisible by 15 , 25 , 40 and 75 = 9999 - 399 = 9600 answer : b
Answer: b
Question (general): a one - foot stick is marked in 1 / 3 and 1 / 4 portion . how many total markings will there be , including the end points ?
Options: a ) 8 , b ) 9 , c ) 7 , d ) 6 , e ) 5
Rationale: "lcm of 12 = 12 1 / 3 marking are ( table of 4 ) 0 . . . . . . 4 . . . . . . 8 . . . . . 12 ( total = 4 ) 1 / 4 marking are ( table of 3 ) 0 . . . . . . . 3 . . . . . . 6 . . . . . . 9 . . . . . . . . 12 ( total = 5 ) overlapping markings are 0 . . . . . . . . 12 ( total = 2 ) total markings = 4 + 5 - 2 = 7 answer = c"
Answer: c
Question (physics): a company has a hierarchical system where for every 10 workers , there is one team lead , and for every 3 teams leads , there is one supervisor . if the company has 13 supervisors , how many workers does it have ?
Options: a ) 140 , b ) 321 , c ) 390 , d ) 500 , e ) 130
Rationale: some students may initially answer 130 to this question , especially if answering similar problems . however , that would be incorrect , as this is not a straight - forward ratio of 1 : 3 : 10 . the ratio of supervisors to team leads is 1 : 3 , and the ratio of team leads to workers is 1 : 10 . therefore , the ratio of supervisors to workers is 1 : 30 . therefore , 13 * 30 = 390 answer : c )
Answer: c
Question (physics): the ratio between the length and the breadth of a rectangular park is 3 : 2 . if a man cycling along the boundary of the park at the speed of 9 km / hr completes one round in 5 min , then the area of the park ( in sq . m ) is ?
Options: a ) 337500 m , b ) 300000 m , c ) 153600 m , d ) 33750 m , e ) 9000 m
Rationale: "perimeter = distance covered in 5 min . = ( 9000 x 5 ) / 60 m = 750 m . let length = 3 x metres and breadth = 2 x metres . then , 2 ( 3 x + 2 x ) = 750 or x = 75 . length = 225 m and breadth = 150 m . area = ( 225 x 150 ) m 2 = 33750 m d"
Answer: d
Question (physics): a train 120 m long is running with a speed of 66 km / hr . in what time will it pass a man who is roller skating at 12 km / hr in the direction opposite to that in which the train is going ?
Options: a ) 4.92 , b ) 6.92 , c ) 7.92 , d ) 4.92 , e ) 2.92
Rationale: "speed of train relative to man = 66 + 12 = 78 km / hr . = 78 * 5 / 18 = 65 / 3 m / sec . time taken to pass the man = 150 * 3 / 65 = 6.92 sec . answer : b"
Answer: b
Question (general): paul ' s income is 20 % less than rex ' s income , quentin ' s income is 20 % less than paul ' s income , and sam ' s income is 40 % less than paul ' s income . if rex gave 60 % of his income to sam and 40 % of his income to quentin , quentin ' s new income would be what fraction of sam ' s new income ?
Options: a ) 26 / 27 , b ) 13 / 17 , c ) 13 / 19 , d ) 12 / 19 , e ) 11 / 19
Rationale: "make r = 10 p = 0.8 r = 8 q = 0.8 p = 6.4 s = 0.6 p = 4.8 for that we get s = 10.8 and q 10.4 so 10.4 / 10.8 = 2.6 / 2.7 ans : a"
Answer: a
Question (general): if a * b denotes the greatest common divisor of a and b , then ( ( 20 * 16 ) * ( 18 * 24 ) ) = ?
Options: a ) 24 , b ) 12 , c ) 6 , d ) 4 , e ) 2
Rationale: "the greatest common divisor of 20 and 16 is 4 . hence 20 * 16 = 4 ( note that * here denotes the function not multiplication ) . the greatest common divisor of 18 and 24 is 6 . hence 18 * 24 = 6 . hence ( ( 20 * 16 ) * ( 18 * 24 ) ) = 4 * 6 . the greatest common divisor of 4 and 6 is 2 . answer ; e ."
Answer: e
Question (general): how many quarters are equal to 2 dollars ?
Options: a ) 1 , b ) 8 , c ) 12 , d ) 9 , e ) 7
Rationale: b . 8 quarters
Answer: b
Question (gain): a person borrows 7000 for 3 years at 6 % p . a . simple interest . he immediately lends it to another person at 31 % p . a . for 3 years . find his gain in the transaction per year .
Options: a ) 1600 , b ) 1700 , c ) 1550 , d ) 1650 , e ) 1750
Rationale: "gain in 3 years = [ ( 7000 ã — 31 ã — 3 / 100 ) â ˆ ’ ( 7000 ã — 6 ã — 3 / 100 ) ] = ( 6510 â € “ 1260 ) = 5250 . â ˆ ´ gain in 1 year = ( 5250 â  „ 3 ) = 1750 answer e"
Answer: e
Question (general): david obtained 86 , 85 , 82 , 87 and 85 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology what are his average marks ?
Options: a ) 75 , b ) 276 , c ) 87 , d ) 85 , e ) 11
Rationale: "explanation : average = ( 86 + 85 + 82 + 87 + 85 ) / 5 = 425 / 5 = 85 . answer : d"
Answer: d
Question (other): how many of the positive factors of 56 , 96 and how many common factors are there in numbers ?
Options: a ) 2 , b ) 4 , c ) 3 , d ) 5 , e ) 1
Rationale: "factors of 56 - 1 , 2 , 4 , 7 , 8 , 14 , 28 , 56 factors of 96 - 1 , 2 , 3 , 4 , 6 , 8 , 12 , 16 , 24 , 32 , 48 , 96 comparing both , we have three common factors of 56 and 96 - 1 , 2,4 answer ( c )"
Answer: c
Question (physics): it takes joey the postman 1 hours to run a 4 mile long route every day . he delivers packages and then returns to the post office along the same path . if the average speed of the round trip is 5 mile / hour , what is the speed with which joey returns ?
Options: a ) 6 2 / 3 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: "let his speed for one half of the journey be 4 miles an hour let the other half be x miles an hour now , avg speed = 5 mile an hour 2 * 4 * x / 4 + x = 5 8 x = 5 x + 20 = > 3 x = 20 = > x = 6 2 / 3 a"
Answer: a
Question (general): a business executive and his client are charging their dinner tab on the executive ' s expense account . the company will only allow them to spend a total of 50 $ for the meal . assuming that they will pay 7 % in sales tax for the meal and leave a 15 % tip , what is the most their food can cost ?
Options: a ) 39.55 $ , b ) 40.63 $ , c ) 41.63 $ , d ) 42.15 $ , e ) 43.15 $
Rationale: "let x be the amount the most their food can cost . x + 0.07 x + 0 . 15 x = 50 solving for x , x = 40.98 $ , this is the maximum amount that can be used for food . hence 40.63 $ is the maximum value less than 40.98 $ hence option b"
Answer: b
Question (general): the sum of present age of abe and the age before 7 years is 37 . find the present age of abe . what will be his age after 7 years ?
Options: a ) 25 , b ) 26 , c ) 27 , d ) 28 , e ) 29
Rationale: "present age = x before 7 yrs , y = x - 7 after 7 yrs , z = x + 7 by the qn , x + ( x - 7 ) = 37 2 x - 7 = 37 2 x = 37 + 7 x = 44 / 2 x = 22 z = x + 7 = 22 + 7 = 29 answer : e"
Answer: e
Question (gain): a retailer bought a machine at a wholesale price of $ 90 and later on sold it after a 10 % discount of the retail price . if the retailer made a profit equivalent to 20 % of the whole price , what is the retail price w of the machine ?
Options: a ) 81 , b ) 100 , c ) 120 , d ) 135 , e ) 160
Rationale: "since the wholesale price was $ 90 and the profit was 20 % of the wholesale price ( [ . 2 ] [ 90 ] = $ 18 ) , the retail price would have to be above $ 108 , but not that much greater than that . let ' s start by testing answer c : $ 120 . . . . if . . . . . retail price w = $ 120 10 % discount off = $ 120 - ( . 1 ) ( 120 ) = 120 - 12 = 108 20 % profit on wholesale price = 90 + ( . 2 ) ( 90 ) = 90 + 18 = 108 these two numbers match , so this must be the answer ! final answer : [ reveal ] spoiler : c"
Answer: c
Question (general): how many kg of pure salt must be added to 100 kg of 10 % solution of salt and water to increase it to a 12 % solution ?
Options: a ) a ) 6.7 , b ) b ) 2.3 , c ) c ) 9.6 , d ) d ) 12.5 , e ) e ) 7.9
Rationale: "amount salt in 100 kg solution = 10 * 100 / 100 = 10 kg let x kg of pure salt be added then ( 10 + x ) / ( 100 + x ) = 12 / 100 250 + 25 x = 300 + 3 x 22 x = 50 x = 2.3 answer is b"
Answer: b
Question (general): what is the total number of integers between 111 and 222 that are divisible by 9 ?
Options: a ) 12 , b ) 10 , c ) 11 , d ) 14 , e ) 13
Rationale: "117 , 126 , 135 , . . . , 207,216 this is an equally spaced list ; you can use the formula : n = ( largest - smallest ) / ( ' space ' ) + 1 = ( 216 - 117 ) / ( 9 ) + 1 = 99 / 9 + 1 = 11 + 1 = 12 answer is a"
Answer: a
Question (gain): 350 is increased by 50 % . find the final number .
Options: a ) 725 , b ) 625 , c ) 225 , d ) 525 , e ) 425
Rationale: explanation final number = initial number + 50 % ( original number ) = 350 + 50 % ( 350 ) = 350 + 175 = 525 . answer d
Answer: d
Question (physics): a train 240 m in length crosses a telegraph post in 16 seconds . the speed of the train is ?
Options: a ) 77 kmph , b ) 55 kmph , c ) 54 kmph , d ) 58 kmph , e ) 76 kmph
Rationale: "s = 240 / 16 * 18 / 5 = 54 kmph answer : c"
Answer: c
Question (physics): a can do a particular work in 6 days . b can do the same work in 8 days . a and b signed to do it for rs . 2400 . they completed the work in 3 days with the help of c . how much is to be paid to c ?
Options: a ) s . 300 , b ) s . 600 , c ) s . 420 , d ) s . 400 , e ) s . 480
Rationale: "explanation : amount of work a can do in 1 day = 1 / 6 amount of work b can do in 1 day = 1 / 8 amount of work a + b can do in 1 day = 1 / 6 + 1 / 8 = 7 / 24 amount of work a + b + c can do = 1 / 3 amount of work c can do in 1 day = 1 / 3 - 7 / 24 = 1 / 24 work a can do in 1 day : work b can do in 1 day : work c can do in 1 day = 1 / 6 : 1 / 8 : 1 / 24 = 4 : 3 : 1 amount to be paid to c = 2400 × ( 1 / 8 ) = 300 answer : option a"
Answer: a
Question (gain): because he ’ s taxed by his home planet , mork pays a tax rate of 45 % on his income , while mindy pays a rate of only 15 % on hers . if mindy earned 4 times as much as mork did , what was their combined tax rate ?
Options: a ) 19 % , b ) 21 % , c ) 23 % , d ) 25 % , e ) 27 %
Rationale: "let x be mork ' s income , then mindy ' s income is 4 x . the total tax paid is 0.45 x + 0.6 x = 1.05 x 1.05 x / 5 x = 0.21 the answer is b ."
Answer: b
Question (geometry): pr is tangent to a circle at point p . q is another point on circle such that pq is diameter of circle and rq cuts circle at m . if radius of circle is 4 units and pr = 6 units . find ratio of triangle pmr to pqr .
Options: a ) 11 / 20
b ) 3 / 5
c ) 13 / 20
d ) 18 / 25
e ) 18 / 26
Rationale: let pm = y qm = x mr = 10 - x in triangle pqm , pm ^ 2 + qm ^ 2 = pq ^ 2 = > x ^ 2 + y ^ 2 = 64 . . . . . ( 1 ) in triangle pmr , pm ^ 2 + mr ^ 2 = pr ^ 2 y ^ 2 + ( 10 - x ) ^ 2 = 36 . . . . . . ( 2 ) solving for x and y x = 6.4 y = 4.8 taking permineter of triangle pqr = 24 perimeter of triangle pmr = 14.4 take ratio 14.4 / 24 = 0.6 answer : c
Answer: c
Question (general): if n is a natural number , then ( 6 n ^ 2 + 6 n ) is always divisible by :
Options: a ) 6 , b ) 12 , c ) 24 , d ) 6 only , e ) 6 and 12 both
Rationale: explanation : ( 6 n ^ 2 + 6 n ) = 6 n ( n + 1 ) , which is always divisible by 6 and 12 both , since n ( n + 1 ) is always even . e
Answer: e
Question (other): the h . c . f . of two numbers is 23 and the other two factors of their l . c . m . are 13 and 17 . the larger of the two numbers is :
Options: a ) 276 , b ) 299 , c ) 391 , d ) 345 , e ) 355
Rationale: "clearly , the numbers are ( 23 x 13 ) and ( 23 x 17 ) . larger number = ( 23 x 17 ) = 391 . answer : option c"
Answer: c
Question (geometry): a rectangular rug with side lengths of 2 feet and 7 feet is placed on a square floor that has an area of 64 square feet . if the surface of the rug does not extend beyond the area of the floor , what fraction of the area of the floor is not covered by the rug ?
Options: a ) a . 3 / 16
b ) 1 / 4
c ) c . 1 / 2
d ) 25 / 32
e ) 7 / 8
Rationale: area of the rectangular rug = 2 * 7 = 14 fraction not covered by the rug = ( total area - rug area ) / total area = ( 64 - 14 ) / 64 = 25 / 32 = d
Answer: d
Question (general): find the value of ( 55 + 113 / 78 ) × 78
Options: a ) 4423 , b ) 4403 , c ) 4413 , d ) 2403 , e ) 4375
Rationale: "= ( 55 + 113 / 78 ) × 78 = ( 4290 + 113 ) / 78 × 78 = 4403 / 78 × 78 = 4403 answer is b ."
Answer: b
Question (physics): if two typists can type two pages in two minutes , how many typists will it take to type 25 pages in 5 minutes ?
Options: a ) 3 , b ) 4 , c ) 10 , d ) 12 , e ) 36
Rationale: in 2 minutes 2 typists type 2 pages which means that in 5 minutes they will type 5 pages but to type 25 pages ( 5 times ) we need 5 times more typists i . e . 2 x 5 = 10 typists . c
Answer: c
Question (general): the total age of a and b is 11 years more than the total age of b and c . c is how many year younger than
Options: a ) 14 years , b ) 12 years , c ) 56 years , d ) 66 years , e ) 11 years
Rationale: "given that a + b = 11 + b + c = > a â € “ c = 11 + b â € “ b = 11 = > c is younger than a by 11 years answer : e"
Answer: e
Question (general): n ^ ( n / 2 ) = 2 is true when n = 2 in the same way what is the value of n if n ^ ( n / 2 ) = 12 ?
Options: a ) 12 , b ) 6 , c ) 14 , d ) 16 , e ) 10
Rationale: n ^ ( n / 2 ) = 12 apply log n / 2 logn = log 12 nlogn = 2 log 12 = log 12 ^ 2 = log 144 logn = log 144 now apply antilog n = 144 / n now n = 12 answer : a
Answer: a
Question (gain): a sum of money at simple interest amounts to rs . 800 in 3 years and to rs . 850 in 4 years . the sum is :
Options: a ) rs . 670 , b ) rs . 690 , c ) rs . 600 , d ) rs . 625 , e ) rs . 654
Rationale: "explanation : s . i . for 1 year = rs . ( 850 - 800 ) = rs . 50 . s . i . for 3 years = rs . ( 50 x 3 ) = rs . 150 . principal = rs . ( 800 - 150 ) = rs . 600 . answer : option c"
Answer: c
Question (general): according to the directions on a packet of smoothie mix , 1 3 - ounce packet of smoothie mix is to be combined with 19 ounces of water to make a smoothie . how many 3 - ounce packets of smoothie mix are required to prepare 150 12 - ounce smoothies ?
Options: a ) 120 , b ) 150 , c ) 180 , d ) 240 , e ) 600
Rationale: "this question was n ' t particularly grueling , but i think it ' s the first where i had the opportunity to solve it via theory andinspectionthat many on this board suggest as strategy on the gmat . it actually came to me by accident . basically , if we thought that the 3 packets of powder were included in the 12 ounces of water , that would mean we would need 150 packets of smoothie mix ( along with 12 ( 150 ) ounces of water for a total of 150 packets . however , we know , after a more careful reading of the stimulus , that the 3 ounces are not included in the 12 ounces . as such , the answer has to be less than 150 packets , since 150 would be too much powder considering you already have 150 ( 12 ) ounces of water and need less packets than water to make a smoothie . as such , the only answer less than 150 is 120 , a . does this make sense ? or am i way off base ? e"
Answer: e
Question (geometry): if y is the smallest positive integer such that 4410 multiplied by y is the square of an integer , then y must be
Options: a ) 2
b ) 5
c ) 6
d ) 7
e ) 10
Rationale: 4410 = 2 * 3 ^ 2 * 5 * 7 ^ 2 to be perfect square , we need to multiply by at least 2 * 5 = 10 . the answer is e .
Answer: e
Question (general): if p and q are positive integers each greater than 1 , and 17 ( p + 1 ) = 20 ( q + 1 ) , what is the least possible value of p + q ?
Options: a ) 35 , b ) 42 , c ) 44 , d ) 46 , e ) none
Rationale: "17 ( p + 1 ) = 29 ( q + 1 ) - - > ( p + 1 ) / ( q + 1 ) = 20 / 17 - - > the least positive value of p + 1 is 20 , so the least value of p is 19 and the least positive value of q + 1 is 17 , so the least value of q is 16 - - > the least value of p + q is 19 + 16 = 35 . answer : a"
Answer: a
Question (gain): a portion of the 80 % solution of chemicals was replaced with an equal amount of 20 % solution of chemicals . as a result , 50 % solution of chemicals resulted . what part of the original solution was replaced ?
Options: a ) 1 / 3 , b ) 1 / 2 , c ) 1 / 4 , d ) 1 / 5 , e ) 1 / 6
Rationale: "this is a weighted average question . say x % of the solution was replaced - - > equate the amount of chemicals : 0.8 ( 1 - x ) + 0.2 * x = 0.5 - - > x = 1 / 2 . answer : b ."
Answer: b
Question (general): the maximum number of students among them 1008 pens and 928 pencils can be distributed in such a way that each student get the same number of pens and same number of pencils ?
Options: a ) 16 , b ) 18 , c ) 36 , d ) 19 , e ) 32
Rationale: "number of pens = 1008 number of pencils = 928 required number of students = h . c . f . of 1008 and 928 = 16 answer is a"
Answer: a
Question (general): lilly has 10 fish and rosy has 12 fish . in total , how many fish do they have in all ?
Options: a ) 18 , b ) 20 , c ) 22 , d ) 24 , e ) 26
Rationale: 10 + 12 = 22 the answer is c .
Answer: c
Question (general): what is the least common multiple of 6 , 18 , and 24 ?
Options: a ) 72 , b ) 120 , c ) 240 , d ) 360 , e ) 720
Rationale: "let us first write the numbers in the form of prime factors : 6 = 2 * 3 18 = 2 * 3 ^ 2 24 = 2 ^ 3 * 3 the lcm would be the largest powers of the prime numbers from all these three numbers . hence lcm = 72 option a"
Answer: a
Question (other): the ratio of number of boys and girls in a school is 2 : 5 . if there are 420 students in the school , find the number of girls in the school ?
Options: a ) 150 , b ) 250 , c ) 300 , d ) 370 , e ) 280
Rationale: "let the number of boys and girls be 2 x and 5 x total students = 420 number of girls in the school = 5 * 420 / 7 = 300 answer is c"
Answer: c
Question (physics): a train covers a distance of 100 km in 1 hour . if its speed is decreased by 20 km / hr , the time taken by the car to cover the same distance will be ?
Options: a ) 1 hr , b ) 1 hr 15 min , c ) 50 min , d ) 1 hr 30 min , e ) 1 hr 45 min
Rationale: speed = 100 / 1 = 100 km / hr new speed = 100 - 20 = 80 km / hr time taken = 100 / 80 = 1 hr 15 min answer is b
Answer: b
Question (probability): a bag contains 3 red , 4 black and 2 white balls . what is the probability of drawing a red and a white ball in two successive draws , each ball being put back after it is drawn ?
Options: a ) 2 / 27 , b ) 1 / 9 , c ) 1 / 3 , d ) 4 / 27 , e ) 2 / 9
Rationale: p = 2 ∗ 39 ∗ 29 = 427 p = 2 ∗ 39 ∗ 29 = 427 we are multiplying by 2 as there are two possible wining scenarios rw and wr . answer : d .
Answer: d
Question (gain): last year sandy saved 10 % of her annual salary . this year , she made 10 % more money than last year , and she saved 15 % of her salary . the amount saved this year was what percent of the amount she saved last year ?
Options: a ) 142 % , b ) 150 % , c ) 165 % , d ) 176 % , e ) 188 %
Rationale: "let last year ' s salary be x . last year , sandy save 0.1 x this year , sandy saved 0.15 * 1.1 x = 0.165 x 0.165 x / 0.1 x = 1.65 = 165 % the answer is c ."
Answer: c
Question (geometry): the volume of a rectangular swimming pool is 840 cubic meters and water is flowing into the swimming pool . if the surface level of the water is rising at the rate of 0.5 meters per minute , what is the rate t , in cubic meters per minutes , at which the water is flowing into the swimming pool ?
Options: a ) 0.125 , b ) 0.25 , c ) 0.5 , d ) 0.75 , e ) not enough information to determine the rate
Rationale: "the correct answer is e . there are not enough info to answer the question . a 840 cubic meters rectangle is built from : height * length * width . from the question we know the volume of the pool and the filling rate . a pool can have a height of 10 * width 8.4 * length 10 and have a volume of 840 cubic meters , and it can have a height of 1 meter , width of 100 meters and length of 8.4 . in both cases the pool will fill up in a different rate = e"
Answer: e
Question (general): the difference between the place values of 7 and 3 in the number 527435 is
Options: a ) 4 , b ) 5 , c ) 45 , d ) 6970 , e ) none
Rationale: "sol . = ( place value of 7 ) – ( place value of 3 ) = ( 700 - 30 ) = 6970 answer d"
Answer: d
Question (general): 15 lts are taken of from a container full of liquid a and replaced with liquid b . again 15 more lts of the mixture is taken and replaced with liquid b . after this process , if the container contains liquid a and b in the ratio 9 : 16 , what is the capacity of the container m ?
Options: a ) a : 45 , b ) b : 25 , c ) c : 37.5 , d ) d : 36 , e ) e : 42
Rationale: "if you have a 37.5 liter capacity , you start with 37.5 l of a and 0 l of b . 1 st replacement after the first replacement you have 37.5 - 15 = 22.5 l of a and 15 l of b . the key is figuring out how many liters of a and b , respectively , are contained in the next 15 liters of mixture to be removed . the current ratio of a to total mixture is 22.5 / 37.5 ; expressed as a fraction this becomes ( 45 / 2 ) / ( 75 / 2 ) , or 45 / 2 * 2 / 75 . canceling the 2 s and factoring out a 5 leaves the ratio as 9 / 15 . note , no need to reduce further as we ' re trying to figure out the amount of a and b in 15 l of solution . 9 / 15 of a means there must be 6 / 15 of b . multiply each respective ratio by 15 to get 9 l of a and 6 l of b in the next 15 l removal . final replacement the next 15 l removal means 9 liters of a and 6 liters of b are removed and replaced with 15 liters of b . 22.5 - 9 = 13.5 liters of a . 15 liters of b - 6 liters + 15 more liters = 24 liters of b . test to the see if the final ratio = 9 / 16 ; 13.5 / 24 = ( 27 / 2 ) * ( 1 / 24 ) = 9 / 16 . choice c is correct ."
Answer: c
Question (physics): a and b together can do a work in 2 days . a alone can do it in 12 days . what time b will take to do the work alone ?
Options: a ) 2.4 days , b ) 8 days , c ) 1.2 days , d ) 1.0 days , e ) 5 days
Rationale: "explanation : a and b 1 day ' s work = 1 / 2 a alone can do 1 day ' s work = 1 / 12 what time b will take to do the work alone ? b = ( a + b ) - a = ( 1 / 2 ) - ( 1 / 12 ) = 2.4 days answer : option a"
Answer: a
Question (general): list k consists of 12 consecutive integers . if - 3 is the least integer in list k , what is the range of the positive integers in list k ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 11 , e ) 12
Rationale: "answer = c = 7 if least = - 3 , then largest = 8 range = 8 - 1 = 7"
Answer: c