Cheukting/mathqa huggingface dataset:
Question (physics): a pump will fill a tank in 3 hours . because of a leak in the tank , it took 3 hours 30 min to fill the tank . in what time the leak can drain out all the water of the tank and will make tank empty ?
Options: a ) 20 hrs , b ) 21 hrs , c ) 22 hrs , d ) 23 hrs , e ) 24 hrs
Rationale: work done for 1 hr without leak = 1 / 3 work done with leak = 31 / 2 = = > 7 / 2 work and leak in 1 hr = 2 / 7 work leak in 1 hr = 1 / 3 - 2 / 7 = 1 / 21 so 21 hrs answer b
Answer: b
Question (geometry): the area of a square garden is q square feet and the perimeter is p feet . if q = p + 21 , what is the perimeter of the garden in feet ?
Options: a ) 24
b ) 28
c ) 32
d ) 36
e ) 40
Rationale: let x be the length of one side of the square garden . x ^ 2 = 4 x + 21 x ^ 2 - 4 x - 21 = 0 ( x - 7 ) ( x + 3 ) = 0 x = 7 , - 3 p = 4 ( 7 ) = 28 the answer is b .
Answer: b
Question (physics): a train 100 m long passes a man , running at 5 km / hr in the same direction in which the train is going , in 10 seconds . the speed of the train is ?
Options: a ) 28 , b ) 50 , c ) 88 , d ) 41 , e ) 12
Rationale: "speed of the train relative to man = ( 100 / 10 ) m / sec = ( 10 ) m / sec . [ ( 10 ) * ( 18 / 5 ) ] km / hr = 36 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 5 ) km / hr . x - 5 = 36 = = > x = 41 km / hr . answer : d"
Answer: d
Question (general): a positive number x is multiplied by 2 , and this product is then divided by 4 . if the positive square root of the result of these two operations equals x , what is the value of x ?
Options: a ) 9 / 4 , b ) 3 / 2 , c ) 4 / 3 , d ) 2 / 3 , e ) 1 / 2
Rationale: "we need to produce an equation from the information given in the problem stem . we are first given that x is multiplied by 2 and then the product is divided by 3 . this gives us : 2 x / 3 next we are given that the positive square root of the result ( which is 2 x / 3 ) is equal to x . this gives us √ ( 2 x / 3 ) = x 2 x / 3 = x ^ 2 2 x = 3 x ^ 2 3 x ^ 2 – 2 x = 0 x ( 3 x – 2 ) = 0 x = 0 or 3 x – 2 = 0 3 x = 2 x = 9 / 4 because x is positive , x = 9 / 4 . the answer is a ."
Answer: a
Question (general): how many multiples of 3 are there between 10 and 100 , exclusive ?
Options: a ) 30 , b ) 29 , c ) 28 , d ) 31 , e ) 33
Rationale: "3 * 4 = 12 3 * 33 = 99 total multiples = ( 33 - 4 ) + 1 = 30 exclude 10 and 100 = 30 answer is a"
Answer: a
Question (gain): an empty fuel tank with a capacity of 200 gallons was filled partially with fuel a and then to capacity with fuel b . fuel a contains 12 % ethanol by volume and fuel b contains 16 % ethanol by volume . if the full fuel tank contains 28 gallons of ethanol , how many gallons of fuel a were added ?
Options: a ) 160 , b ) 150 , c ) 100 , d ) 80 , e ) 50
Rationale: "say there are a gallons of fuel a in the tank , then there would be 200 - a gallons of fuel b . the amount of ethanol in a gallons of fuel a is 0.12 a ; the amount of ethanol in 200 - a gallons of fuel b is 0.16 ( 200 - a ) ; since the total amount of ethanol is 28 gallons then 0.12 a + 0.16 ( 200 - a ) = 28 - - > a = 100 . answer : c ."
Answer: c
Question (physics): maxwell leaves his home and walks toward brad ' s house . one hour later , brad leaves his home and runs toward maxwell ' s house . if the distance between their homes is 14 kilometers , maxwell ' s walking speed is 4 km / h , and brad ' s running speed is 6 km / h . what is the total time it takes maxwell before he meets up with brad ?
Options: a ) 2 , b ) 4 , c ) 5 , d ) 6 , e ) 8
Rationale: total distance = 14 kms maxwell speed = 4 kms / hr maxwell travelled for 1 hour before brad started , therefore maxwell traveled for 4 kms in 1 hour . time taken = total distance / relative speed total distance after brad started = 10 kms relative speed ( opposite side ) ( as they are moving towards each other speed would be added ) = 6 + 4 = 10 kms / hr time taken to meet brad after brad started = 10 / 10 = 1 hrs distance traveled by maxwell = maxwell ' s speed * time taken = 4 * 1 = 4 + 4 = 8 kms . . . therefore total time taken by maxwell to meet brad = distance travelled by maxwell / maxwell ' s speed = 8 / 4 = 2 hrs . . . answer a
Answer: a
Question (general): the total price of a basic computer and printer are $ 2,500 . if the same printer had been purchased with an enhanced computer whose price was $ 500 more than the price of the basic computer , then the price of the printer would have been 2 / 5 of that total . what was the price of the basic computer ?
Options: a ) 1300 , b ) 1600 , c ) 1750 , d ) 1900 , e ) 2000
Rationale: "let the price of basic computer be c and the price of the printer be p : c + p = $ 2,500 . the price of the enhanced computer will be c + 500 and total price for that computer and the printer will be 2,500 + 500 = $ 3,000 . now , we are told that the price of the printer is 2 / 5 of that new total price : p = 2 / 5 * $ 3,000 = $ 1200 . plug this value in the first equation : c + 1200 = $ 2,500 - - > c = $ 1,300 . answer : a ."
Answer: a
Question (probability): in a lottery there are 20 prizes and 35 blanks . a lottery is drawn at random . what is the probability of getting a prize
Options: a ) 2 / 13 , b ) 4 / 11 , c ) 5 / 11 , d ) 6 / 11 , e ) 3 / 13
Rationale: "total draws = prizes + blanks = 20 + 35 = 55 probability of getting a prize = 20 / 55 = 4 / 11 correct option is b"
Answer: b
Question (physics): lloyd normally works 7.5 hours per day and earns $ 3.50 per hour . for each hour he works in excess of 7.5 hours on a given day , he is paid 1.5 times his regular rate . if lloyd works 10.5 hours on a given day , how much does he earn for that day ?
Options: a ) $ 33.75 , b ) $ 42.00 , c ) $ 51.75 , d ) $ 54.00 , e ) $ 70.00
Rationale: "daily working hour * regular rate + overtime * increased rate 7.5 * 3.5 + 3 * 3.5 * 1.5 = 42 answer b"
Answer: b
Question (physics): tammy climbed a mountain in two days . she spent a total of 14 hours climbing the mountain . on the second day , she walked at an average speed that was half a kilometer per hour faster , but 2 hours less than what she walked on the first day . if the total distance she climbed during the two days is 52 kilometers , how many e kilometers per hour did tammy walk on the second day ?
Options: a ) 3 , b ) 3.5 , c ) 4 , d ) 4.5 , e ) 6
Rationale: ans : c total time = 14 hrs let time traveled during 1 st day = x let time traveled during 2 nd day = x - 2 total time = 14 x + x - 2 = 14 x = 8 speed * time = distance s * 8 + ( s + 0.5 ) ( 8 - 2 ) = 52 solving s = 4.5 now speed for 2 nd day is 0.5 less than the 1 st day which is 4.5 thus speed for 2 nd day = 4 its simple algebra for s * 8 + ( s + 0.5 ) ( 8 - 2 ) = 52 but for some reason im getting 3.5 and not 4.5 . 8 s + 6 s + 3 = 52 14 s = 49 s = 3.5
Answer: c
Question (physics): the l . c . m of two numbers is 2310 and their h . c . f is 30 . if one number is 462 the other is
Options: a ) 330 , b ) 300 , c ) 270 , d ) 150 , e ) 350
Rationale: "the other number = l . c . m * h . c . f / given number = 2310 * 30 / 462 = 150 answer is d ."
Answer: d
Question (gain): a reduction of 22 % in the price of salt enables a lady to obtain 10 kgs more for rs . 100 , find the original price per kg ?
Options: a ) s . 2.82 , b ) s . 2.4 , c ) s . 2.5 , d ) s . 2.2 , e ) s . 2.1
Rationale: "100 * ( 22 / 100 ) = 22 - - - 10 ? - - - 1 = > rs . 2.2 100 - - - 78 ? - - - 2.2 = > rs . 2.82 answer : a"
Answer: a
Question (gain): a person incurs a loss of 5 % be selling a watch for rs . 1140 . at what price should the watch be sold to earn 5 % profit .
Options: a ) rs . 1200 , b ) rs . 1230 , c ) rs . 1260 , d ) rs . 1290 , e ) rs . 1270
Rationale: explanation : let the new s . p . be x , then . ( 100 - loss % ) : ( 1 st s . p . ) = ( 100 + gain % ) : ( 2 nd s . p . ) = > ( 951 / 140 = 105 / x ) = > x = 1260 answer is c
Answer: c
Question (physics): patanjali walked for 3 days . she walked 18 miles on the first day , walking 3 miles per hour . on the second day she walked for one less hour but she walked one mile per hour , faster than on the first day . on the third day she walked the same number of hours as on the first day , but at the same speed as on the second day . how many miles in total did she walk ?
Options: a ) 24 , b ) 44 , c ) 58 , d ) 60 , e ) 62
Rationale: patanjali walked 18 miles on the first day , walking 3 miles per hour i . e . total time of walk on day - 1 = 18 / 3 = 6 hours second day time of walk = 6 - 1 = 5 hours and speed = 3 + 1 = 4 miles per hour i . e . distance walked on second day = 5 * 4 = 20 miles third day time of walk = 6 hours and speed = 4 miles per hour i . e . distance walked on second day = 6 * 4 = 24 miles total distance travelled on three days = 18 + 20 + 24 = 62 answer : option e
Answer: e
Question (physics): the current in a river is 10 mph . a boat can travel 50 mph in still water . how far up the river can the boat travel if the round trip is to take 5 hours ?
Options: a ) 120 , b ) 100 , c ) 96 , d ) 85 , e ) 150
Rationale: upstream speed = 50 - 10 = 40 mph downstream speed = 50 + 10 = 60 mph d / 40 + d / 60 = 5 hours solving for d we get d = 120 answer : a
Answer: a
Question (general): 60 is to be divided into two parts such that the sum of 10 times the first and 22 times the second is 780 . the bigger part is :
Options: a ) 33 , b ) 45 , c ) 26 , d ) 28 , e ) 19
Rationale: "explanation : let the two parts be ( 60 - x ) and x . then , 10 ( 60 - x ) + 22 x = 780 = > 12 x = 180 = > x = 15 . bigger part = ( 60 - x ) = 45 . answer : b ) 45"
Answer: b
Question (general): the sum of two number is 25 and their difference is 13 . find their product .
Options: a ) 114 , b ) 104 , c ) 315 , d ) 350 , e ) 400
Rationale: "let the numbers be x and y . then , x + y = 25 and x - y = 13 . 4 xy = ( x + y ) 2 - ( x - y ) 2 = ( 25 ) 2 - ( 13 ) 2 = ( 625 - 169 ) = = 456 = > 114 answer a"
Answer: a
Question (gain): a library branch originally contained 18360 volumes , 30 % of which were fiction novels . 1 / 3 of the volumes were transferred to another location and 1 / 5 of the volumes transferred were fiction novels . what percent of the remaining collection was fiction novels ?
Options: a ) 2.5 % , b ) 17.67 % , c ) 28.3 % , d ) 36 % , e ) 73.6 %
Rationale: fiction novels = 5,508 transferred to another location = 6,120 transferred fiction novels = 1,101 non transferred fiction novels = 4,407 percent of the remaining collection was fiction novels = 4,407 / ( 18360 - 6120 ) * 100 = > 36.004 . . . % hence answer will be ( d )
Answer: d
Question (general): there is one 4 - digit whole number n , such that the last 4 digits of n 2 are in fact the original number n
Options: a ) 8476 , b ) 7376 , c ) 9376 , d ) 7378 , e ) 9466
Rationale: c 9376 looking at the last digit , the last digit must be either 0 , 1 , 5 or 6 . then looking at the last two digits , the last two digits must be either 0001 , 25 or 76 . then looking at the last three digits , the last three digits must be either 00001 , 625 or 376 . then looking at the last four digits , the last four digits must be either 0000001 , 0625 or 9376 . out of those , only 9376 is a 4 digit number
Answer: c
Question (probability): when two dice are tossed , what is the probability that the total score is a prime number ?
Options: a ) 1 / 6 , b ) 3 , c ) 5 / 12 , d ) 7 / 12 , e ) 9 / 12
Rationale: total number of outcomes possible = 36 probability of total score is a prime number = 15 p ( e ) = 15 / 36 = 5 / 12 answer : c
Answer: c
Question (gain): running at the same constant rate , 6 identical machines can produce a total of 420 bottles per minute . at this rate , how many bottles could 10 such machines produce in 4 minutes ?
Options: a ) 648 , b ) 1800 , c ) 2800 , d ) 10800 , e ) 10900
Rationale: "let the required number of bottles be x . more machines , more bottles ( direct proportion ) more minutes , more bottles ( direct proportion ) machines 6 : 10 : : 420 : x time ( in minutes ) 1 : 4 6 x 1 x x = 10 x 4 x 420 x = ( 10 x 4 x 420 ) / ( 6 ) x = 2800 . answer : c"
Answer: c
Question (physics): there is food for 760 men for 22 days . how many more men should join after two days so that the same food may last for 5 days more ?
Options: a ) 2280 , b ) 2240 , c ) 2299 , d ) 2288 , e ) 2266
Rationale: "760 - - - - 22 760 - - - - 20 x - - - - - 5 x * 5 = 760 * 20 x = 3040 760 - - - - - - - 2280 answer : a"
Answer: a
Question (geometry): the ratio of the volumes of two cubes is 216 : 343 . what is the ratio of their total surface areas ?
Options: a ) 81 : 12 , b ) 31 : 36 , c ) 81 : 22 , d ) 8 : 19 , e ) 1 : 11
Rationale: "ratio of the sides = ³ √ 216 : ³ √ 343 = 6 : 7 ratio of surface areas = 62 : 72 = 31 : 36 answer : b"
Answer: b
Question (geometry): the length and breadth of a rectangle is increased by 10 % and 30 % respectively . what is the increase in the area ?
Options: a ) 43.0 , b ) 44.0 , c ) 43.5 , d ) 45.0 , e ) 42.0
Rationale: "100 * 100 = 10000 110 * 130 = 14300 - - - - - - - - - - 4300 10000 - - - - - - - 4300 100 - - - - - - - 43.00 answer a"
Answer: a
Question (physics): the distance between 2 cities a and b is 1000 km . a train starts from a at 11 a . m . and travels towards b at 100 km / hr . another starts from b at 12 p . m . and travels towards a at 150 km / hr . at what time do they meet ?
Options: a ) 11 am . , b ) 12 p . m . , c ) 3 pm . , d ) 4 p . m . , e ) 1 p . m .
Rationale: "suppose they meet x hrs after 11 a . m . distance moved by first in x hrs + distance moved by second in ( x - 1 ) hrs = 1000 100 x + 150 ( x - 1 ) = 1000 x = 4.60 = 5 hrs they meet at 11 + 5 = 4 p . m . answer is d"
Answer: d
Question (general): in the number 11,0 ab , a and b represent the tens and units digits , respectively . if 11,0 ab is divisible by 65 , what is the greatest possible value of b × a ?
Options: a ) 0 , b ) 5 , c ) 10 , d ) 15 , e ) 25
Rationale: "you should notice that 65 * 2 = 110 so 11,000 is divisible by 55 : 55 * 200 = 11,000 ( or you can notice that 11,000 is obviously divisible by both 5 and 11 so by 55 ) - - > b * a = 0 * 0 = 0 . next number divisible by 55 is 11,000 + 55 = 11,055 : b * a = 5 * 2 = 10 ( next number wo n ' t have 110 as the first 3 digits so we have only two options 0 and 25 ) . answer : c ! please post ps questions in the ps subforum : gmat - problem - solving - ps - 140 / please post ds questions in the ds subforum : gmat - data - sufficiency - ds - 141 / no posting of ps / ds questions is allowed in the mainmath forum . c"
Answer: c
Question (general): if k is the greatest positive integer such that 3 ^ k is a divisor of 15 ! then k =
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: for solving this type of tasks we can use such approach 15 / 3 = 5 15 / 3 ^ 2 = 1 and remainder and 3 ^ 3 is more than 15 so we stop on second exponent 5 + 1 = 6 so maximum value of k = 6 and answer is d
Answer: d
Question (general): how many of the integers between 15 and 55 are even ?
Options: a ) 21 , b ) 20 , c ) 11 , d ) 10 , e ) 9
Rationale: "number start between 15 to 55 is 40 numbers half of them is even . . which is 20 answer : b"
Answer: b
Question (general): count the numbers between 10 - 99 which yield a remainder of 5 when divided by 8 and also yield a remainder of 1 when divided by 6 ?
Options: a ) one , b ) three , c ) two , d ) five , e ) four
Rationale: "answer = e ) four numbers between 10 - 99 giving remainder 5 when divided by 8 = 13 , 21 , 29 , 37 , 45 , 53 , 61 , 69 , 77 , 85 , 93 the above numbers giving remainder 1 when divided by 6 = 13 , 37 , 61 , 85 = 4"
Answer: e
Question (physics): a train 510 m long is running at a speed of 45 km / hr . in what time will it pass a bridge 140 m long ?
Options: a ) 40 , b ) 52 , c ) 26 , d ) 21 , e ) 14
Rationale: "speed = 45 * 5 / 18 = 25 / 2 m / sec total distance covered = 510 + 140 = 650 m required time = 650 * 2 / 25 = 52 sec answer : b"
Answer: b
Question (other): if ryan and smith car ratio is 5 : 8 . ryan bought 6 new car and smith bought 2 new car . now , smith has 18 car . what is their car ratio now ?
Options: a ) 5 : 4 , b ) 3 : 2 , c ) 8 : 9 , d ) 6 : 5 , e ) 7 : 5
Rationale: current no . of smith car = 8 x + 2 = 18,8 x = 16 , x = 2 . current car ratio = 10 + 6 / 18 = 16 / 18 = 8 : 9 . answer c
Answer: c
Question (general): a ( 7 , w ^ 3 ) is the ( x , y ) coordinate of point located on the parabola y = x ^ 2 + 15 . what is the value of w ?
Options: a ) 3 . , b ) 4 . , c ) 5 . , d ) 6 . , e ) 9 .
Rationale: "y = x ^ 2 + 15 w ^ 3 = 7 ^ 2 + 15 w ^ 3 = 64 w = 4 answer b"
Answer: b
Question (physics): the timing of a college is from 12 p . m to 4.10 p . m . five lectures are held in the given duration and a break of 5 minutes after each lecture is given to the students . find the duration of each lecture .
Options: a ) 52 minutes , b ) 45 minutes , c ) 46 minutes , d ) 48 minutes , e ) 44 minutes
Rationale: "explanation : total time a student spends in college = 4 hours 10 minutes = 250 minutes as there are 5 lectures , the number of breaks between lectures is 4 . total time of the break = 20 minutes hence , the duration of each lecture is = ( 250 â € “ 20 ) / 5 = 46 minutes answer c"
Answer: c
Question (general): the grade point average of one third of the classroom is 45 ; the grade point average of the rest is 60 . what is the grade point average of the whole class ?
Options: a ) 54 , b ) 55 , c ) 60 , d ) 65 , e ) 70
Rationale: let n = total students in class total points for 1 / 3 class = 45 n / 3 = 15 n total points for 2 / 3 class = 60 * 2 n / 3 = 40 n total points for whole class = 15 n + 40 n = 55 n 63 n total class points / n total students = 55 grade point average for total class answer : b
Answer: b
Question (physics): 63 persons can repair a road in 12 days , working 5 hours a day . in how many days will 30 persons , working 6 hours a day , complete the work ?
Options: a ) 21 , b ) 23 , c ) 24 , d ) 25 , e ) 26
Rationale: "according to the chain rule , m 1 x t 1 = m 2 x t 2 therefore , 63 x 12 x 5 = 30 x 6 x x x = 21 hence , the number of days = 21 . answer : a"
Answer: a
Question (general): marcella has 24 pairs of shoes . if she loses 9 individual shoes , what is the greatest number of matching pairs she could have left ?
Options: a ) 21 , b ) 20 , c ) 19 , d ) 16 , e ) 15
Rationale: "marcella has 24 pairs of shoes and loses 9 shoes . to minimize the loss of identical pairs of shoes we want marcella to lose as many identical pairs as possible . this would yield 4 identical pairs and 1 additional shoe ( destroying 5 pairs of shoes ) . the 24 pairs of shoes minus the 5 ' destroyed ' pairs yields 19 pairs that still fulfill the requirements . answer : c"
Answer: c
Question (general): the sum of the squares of three numbers is 138 , while the sum of their products take two at a time is 131 . find the sum ?
Options: a ) 10 , b ) 30 , c ) 20 , d ) 50 , e ) 40
Rationale: "formula is ( a + b + c ) ^ 2 = ( a ^ 2 ) + ( b ^ 2 ) + ( c ^ 2 ) + 2 ( ab + bc + ca ) = 138 + ( 2 * 131 ) the sum of the three numbers a + b + c = √ 400 = 20 answer is option c"
Answer: c
Question (physics): two trains are approaching each other at 60 mph each . the length of each train is 1 / 6 miles . when the two locomotives ( engines ) meet , how many seconds will it take for them to pass each other completely ?
Options: a ) 8 sec , b ) 11 sec , c ) 12 sec , d ) 10 sec , e ) 15 sec
Rationale: total distance to cover = 2 * ( 1 / 6 ) = 2 / 6 miles relative speed = 60 + 60 = 120 mph time taken = ( 2 / 6 ) / 120 * 3600 = 10 sec . answer : d
Answer: d
Question (physics): a courtyard is 25 meter long and 15 meter board is to be paved with bricks of dimensions 20 cm by 10 cm . the total number of bricks required is ?
Options: a ) 22877 , b ) 27778 , c ) 18750 , d ) 27999 , e ) 17799
Rationale: "number of bricks = courtyard area / 1 brick area = ( 2500 × 1500 / 20 × 10 ) = 18750 answer : c"
Answer: c
Question (gain): a team won 50 percent of its first 60 games in a particular season , and 80 percent of its remaining games . if the team won a total of 70 percent of its games that season , what was the total number of games that the team played ?
Options: a ) 75 , b ) 90 , c ) 120 , d ) 150 , e ) 180
Rationale: "70 % is 20 % - points above 50 % and 10 % - points below 80 % . thus the ratio of ` ` the first 60 games ' ' to ` ` remaining games ' ' is 1 : 2 . so the team played a total of 60 + 120 = 180 games . the answer is e ."
Answer: e
Question (geometry): if k and w are the dimensions of a rectangle that has area 48 , and if k and w are integers such that k > w , what is the total number of possible values of k ?
Options: a ) four , b ) three , c ) two , d ) five , e ) six
Rationale: "kw = 48 = 48 * 1 = 24 * 2 = 16 * 3 = 12 * 4 - - > k can take 4 values . answer : a"
Answer: a
Question (general): a number when divided by 5 , gives 45 as quotient and 0 as remainder . what will be the remainder when dividing the same number by 10
Options: a ) a ) 5 , b ) b ) 3 , c ) c ) 4 , d ) d ) 6 , e ) e ) 7
Rationale: "explanation : p ÷ 5 = 45 = > p = 45 * 5 = 225 p / 10 = 225 / 10 = 22 , remainder = 5 answer : option a"
Answer: a
Question (general): a certain elevator has a safe weight limit of 1950 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 190 pounds and the average weight of the others being 200 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 190 and other half has 200 . maximum weight is = 1950 so 190 * x + 200 * x = 1950 = > 390 x = 1950 = > x is approximately equal to 5 . so total people is 2 * 5 = 10 answer d ."
Answer: d
Question (gain): a and b invests rs . 8000 and rs . 12000 in a business . after 4 months , a withdraws half of his capital and 2 months later , b withdraws one - third of his capital . in what ratio should they share the profits at the end of the year ?
Options: a ) 32 : 99 , b ) 82 : 31 , c ) 8 : 15 , d ) 34 : 89 , e ) 35 : 21
Rationale: a : b ( 8000 * 4 ) + ( 4000 * 8 ) : ( 12000 * 6 ) + ( 9000 * 6 ) 64000 : 120000 8 : 15 answer : c
Answer: c
Question (physics): the height of the wall is 6 times its width and length of the wall is 7 times its height . if the volume of the wall be 86436 cu . m . its width is
Options: a ) 4 m , b ) 5 m , c ) 6 m , d ) 7 m , e ) 8 m
Rationale: "explanation : let width = x then , height = 6 x and length = 42 x 42 x ã — 6 x ã — x = 86436 x = 7 answer : d"
Answer: d
Question (gain): money invested at x % , compounded annually , triples in value in approximately every 112 / x years . if $ 2000 is invested at a rate of 8 % , compounded annually , what will be its approximate worth in 28 years ?
Options: a ) $ 3,750 , b ) $ 5,600 , c ) $ 8,100 , d ) $ 18,000 , e ) $ 22,500
Rationale: "x = 8 % 112 / x years = 112 / 8 = 14 years now , money triples every 14 years therefore , in 14 yrs , if $ 2000 triples to $ 6000 , in 28 years , it will again triple to $ 6000 * 3 = $ 18,000 answer d"
Answer: d
Question (gain): a man buys rs . 44 shares paying 9 % dividend . the man wants to have an interest of 12 % on his money . the market value of each share is :
Options: a ) s . 12 , b ) s . 15 , c ) s . 18 , d ) s . 21 , e ) s . 33
Rationale: "dividend on rs . 44 = rs . 9 / 100 x 44 = rs . 3.96 . rs . 12 is an income on rs . 100 . rs . 3.96 is an income on rs . 100 / 12 x 3.96 = rs . 33 . answer : option e"
Answer: e
Question (physics): water is leaking out from a cylinder container at the rate of 0.31 m ^ 3 per minute . after 10 minutes , the water level decreases 1 / 16 meters . what is value of the radius in meters ?
Options: a ) 1 / 4 , b ) 2 , c ) 4 , d ) 8 , e ) 12
Rationale: "10 * 0.31 = 3.1 = pi * r ^ 2 * h r ^ 2 = 3.1 / ( pi * 1 / 16 ) which is about 16 r = 4 the answer is c ."
Answer: c
Question (other): the duplicate ratio of 4 : 5 is ?
Options: a ) 1 : 2 , b ) 1 : 4 , c ) 1 : 8 , d ) 1 : 18 , e ) 16 : 25
Rationale: 4 ^ 2 : 5 ^ 2 = 16 : 25 answer : e
Answer: e