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Problem Solving
  1. One inlet pipe fills an empty pond in 5 hours. A second inlet pipe fills the same tank in 3 hours. If both pipes are used together, how long will it takes to fill 2/3 of the tank?
    A. 8/15 hr
    B. 3/4 hr
    C. 5/4 hr
    D. 15/8 hr
    E. 8/3 hr
     
  2. Coins are dropped into a toll box so that the box is being filled at the rate of approximately 2 cubic feet per hour. If the empty rectangular box is 4 feet long, 4 feet wide, and 3 feet deep, approximately how many hours does it take to fill the box?
    A. 4
    B. 8
    C. 16
    D. 24
    E. 48
     
  3. Machine A produces books at a constant rate of 120 in 40 seconds, and machine B produces books at the rate of 100 in 20 seconds. If the two machines run at the same time, how long (in seconds) will it take them to produce 200 books?
    A. 22
    B. 25
    C. 28
    D. 32
    E. 56
     
  4. If a photocopier makes 2 copies in 1/3 second, how many copies does it take in 4 minutes?
    A. 360
    B. 480
    C. 576
    D. 720
    E. 1440
     
  5. An empty pool being filled with water at a constant rate takes 8 hours to fill to 3/5 of its capacity. How much more time will it take to finish filling the pool?
    A. 5 hr 30 min
    B. 5 hr 20 min
    C. 4 hr 48 min
    D. 3 hr 12 min
    E. 2 hr 40 min
     
  6. A, B and C, individually, can wash a car in 4, 5 and 6 hours, respectively. What is the greatest part of the job that can be done in one hour by two of them working together at their respective rates?
    A. 11/30
    B. 9/20
    C. 3/5
    D. 11/15
    E. 5/6

Data Sufficiency
  1. Hoses X and Y simultaneously fill an empty swimming pool that has a capacity of 50000 liters. If the flow in each hose is independent of the flow in the other hose, how many hours will it take to fill the pool?
    (1) Hose X alone would take 28 hours to fill the pool
    (2) Hose Y alone would take 36 hours to fill the pool.
     
  2. On Friday morning a certain machine ran continuously at a uniform rate to fill a production order. At what time did it completely fill the order that morning?
    (1) The machine began filling the order at 9:30 a.m.
    (2) The machine had filled 1/2 of the order by 10:30 a.m. and 5/6 of the order by 11:10 a.m.

Answers:

Problem Solving

  1. Let A and B are the first and second pipes respectively
    Equation           1/5 + 1/3 = 1/t                  when t is the time A & B are used together to fill the tank.
                                            t = 15/8 hr.
    But we need just 2/3 of the tank; the time is = 2/3 x 15/8 = 5/4 hr.   C.
     
  2. First of all, find the volume of the box, which is = 4 x 4 x 3 = 48 cu.f. (A trick, basically you don’t have to waste time find the product of 4 x 4 x 3 at this occasion since it’s quite likely that these figures will be readily used in another stage).
    Equation          time = work / rate   in which work = the volume
                              time = 4 x 4 x 3 / 2 = 24 hr. D.
     
  3. Like 1,               120/40 + 100/20 = 200/t
                                                       t  = 200/8 = 25 seconds. B
     
  4. Like 2, rate = work / time = 2 / (1/3) = 6 copies/sec.
                work = rate x time = 6 x 4 x 60 = 1440 copies. (Make sure you change the unit correctly) E.
     
  5. Like 4, rate = work / time = (3/5) / 8 = 3/40 pool/hr. It means in one hour you can make it 3/40 of the pool or you need 40/3 hour to fill the whole pool. The time remaining to fill the pool is = 40/3 - 8 = 16/3 hr. = 5 hr. and 20 min. B.
     
  6. Firstly, you have two choose which two of the three to work together. To get the greatest part of the job, you need the fastest two, that is, A and B. Then, go to our equation
                         1/4 + 1/5 = rate of A and B working together
                                         = 9/20; that is in one hour A & B working together will complete 9/20 part of the job.B.

Data Sufficiency

  1. Simply write the equation first, 50000/X + 50000/Y = 50000/T, when T is the time X & Y working together. To find T you absolutely need both X and Y. C is the right answer.
     
  2. Rarely get anything from the question. So move on to the info.
    (1) You know just the time it began. Nothing much.
    (2) seems to give much more than expected. Let’s analyze it.
            From 10:30 to 11:10 (40 min.), it completed jobs by 5/6 - 1/2 = ? You don’t absolutely need to compute it. Just assume that you
           know it. So now you know the rate of the machine. You know that from 10:30 the order required was 1/2 and you know the
           rate and then you can find the time needed to complete such order by: time = work / rate. I hope you can find the time it
          finished the job. As a result B is the answer.

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Last updated: Sep 18, 2001