Hoses X and Y simultaneously fill an empty swimming pool

Question

Hoses X and Y simultaneously fill an empty swimming pool that has a capacity of 50,000 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.

(1) Hose X alone would take 28 hours to fill the pool.
(2) Hose Y alone would take 36 hours to fill the pool.

Bunuel · Answer

SOLUTION

Hoses X and Y simultaneously fill an empty swimming pool that has a capacity of 50,000 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.

We have the amount of the work to be done, hence to answer the question we need the rates of both hoses X and Y.

(1) Hose X alone would take 28 hours to fill the pool. We have the rate of hose X only. Not sufficient.
(2) Hose Y alone would take 36 hours to fill the pool. We have the rate of hose Y only. Not sufficient.

(1)+(2) We have both rates. Sufficient.

Answer: C.

beatthegmat05 · Answer

Hose X fills 1/28 pool in one hour.
Hose Y fills 1/36 pool in one hour.

Combine X and Y will fill 1/28+1/36 pool in our.Say this comes out to be (a/b) pool in one hour.

To fill full pool it will require 1/(a/b) hours which is b/a .

So answer is (D)

BabySmurf · Answer

Answer has to be (C).

Rate-work-formula: R*T=W
W = 50,000 liters

Rx = Rate of hose x
Ry = Rate of hose y
Rt = Combined rate of both hoses = Rx + Ry

Question: Given Rt * T = 50,000 what is T?

Statement (1) allows you to calculate Rx: Rx = 50,000/26. But you have no information about Ry.  Not sufficient. 
Statement (2) allows you to calculate Ry: Ry = 50,000/36. But you have no information about Rx.  Not sufficient.

Combined, you can calculate each rate and add them to get Ry. You then can calculate the time T = 50,000/Rt.

You actually do not need to do any of these calculations. Just imagining the requirement in your head (without even writing down anything), you can see quickly that answer is C.

Btw. I feel question is Sub-600 difficulty.

BabySmurf · Answer

Your answer includes "b/a hours", which is a variable. I think the question asks for a specific number of hours. 
You need both statements to get that.

cherukuri1011 · Answer

Hoses X and Y simultaneously fill an empty swimming pool that has a capacity of 50,000 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.

(1) Hose X alone would take 28 hours to fill the pool.
(2) Hose Y alone would take 36 hours to fill the pool.

The answer is C. The solution is as follows.
1.(1) Hose X alone would take 28 hours to fill the pool - Insufficient as we are not aware at what rate the other hose fills the pool (Its like when two persons are doing the work we cant calculate how much time it takes to complete as we donot know the other persons working capability)
2.(2) Hose Y alone would take 36 hours to fill the pool. -- Insufficient
Now considering both 1 & 2 we know what rate both hose fill and will be sufficient to answer the question.
The quantitative solution is as follows.
Hose X fills tank in 28 hours so it fills 1/28 of the tank in an hour.
Hose Y fills tank in 36 hours so it fills 1/36 of tank in an hour.
they both together fills (1/28) +(1/36) =(16/252) =4/63. i.e they together fill 4/63 of tank in an hour.
To fill entire tank simultaneously they take 63/4 hours .
Hope only concept is sufficient to answer the question

stne · Answer

let A be the Hours taken by hose X alone to fill the pool.
Let B be the hours taken by hose Y alone to fill the pool.

So working together the time taken to fill the pool is given by  \frac{1}{A}+\frac{1}{B}=\frac{1}{T} 
Where T is the time taken together to fill the pool.

(1) Hose X alone would take 28 hours to fill the pool.
We are given A no info of B insufficient.

(2) Hose Y alone would take 36 hours to fill the pool.
we are given B no info of A insufficient.

1+2

we have both A and B hence we can calculate T using
 \frac{1}{28}+\frac{1}{36}= \frac{1}{T}

Sufficient 
Answer C

Dienekes · Answer

One point worth mentioning here is that one actually does not require the value of total amount of work (i.e. 50,000 litres) to answer this question. The way statements I and II are written, whether the total capacity is 50,000 or 10 litres, the answer will be the same.

zjhon · Answer

Hose X fills 1/28 of the pool in one hour, and Hose Y fills 1/36 of the pool in one hour.

When combined, X and Y together fill $ \frac{1}{28} + \frac{1}{36} $ of the pool in one hour. Simplifying this sum, we get $ \frac{a}{b} $ of the pool per hour.

To fill the entire pool, the time required will be the reciprocal of $ \frac{a}{b} $, which is $ \frac{b}{a} $ hours.

Therefore, the answer is (D).

BlackHat098 · Answer

spent over more than 2 mins, trying to find there must be some nuance attached to the question and that it could be a possible C trap question, as Bunuel would have hidden some trick somewhere, overthinking doesn't always work in your favour I guess.

totaltestprepNick · Answer

C https://www.youtube.com/watch?v=puei8hTnn8o Nick Slavkovich, GMAT/GRE tutor with 20+ years of experience tutoring@totaltestprep.net

Hoses X and Y simultaneously fill an empty swimming pool

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