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An empty swimming pool with a capacity of 75,000 liters is [#permalink]
01 Apr 2012, 15:06

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Difficulty:

25% (medium)

Question Stats:

68% (02:11) correct
32% (01:14) wrong based on 587 sessions

An empty swimming pool with a capacity of 75,000 liters is to be filled by hoses X and Y simultaneously. If the amount of water flowing from each hose is independent of the amount flowing from the other hose, how long, in hours, will it take to fi ll the pool?

(1) If hose X stopped fi lling the pool after hoses X and Y had filled half the pool, it would take 21 hours to fi ll the pool. (2) If hose Y stopped fi lling the pool after hoses X and Y had filled half the pool, it would take 16 hours to fi ll the pool.

An empty swimming pool with a capacity of 75,000 liters is to be filled by hoses X and Y simultaneously. If the amount of water flowing from each hose is independent of the amount flowing from the other hose, how long, in hours, will it take to fi ll the pool?

(1) If hose X stopped fi lling the pool after hoses X and Y had filled half the pool, it would take 21 hours to fi ll the pool. After hose X stops, hose Y continues filling the remaining half of the pool alone, and we are told that it needs 21 hours for that, hence to fill the whole pool it needs 21*2=42 hours. We know the rate of Y, though know nothing about the rate of X. Not sufficient.

(2) If hose Y stopped fi lling the pool after hoses X and Y had filled half the pool, it would take 16 hours to fi ll the pool. Reverse case: after hose Y stops, hose X continues filling the remaining half of the pool alone, and we are told that it needs 16 hours for that, hence to fill the whole pool it needs 16*2=32 hours. We know the rate of X, though know nothing about the rate of Y. Not sufficient.

(1)+(2) We know the rates of both hose X and Y, hence we can calculate the time they'll need to fi ll the pool of 75,000 liters. Sufficient.

Re: An empty swimming pool with a capacity of 75,000 liters is [#permalink]
31 May 2013, 07:55

I was a bit confused with this question. My interpretation of the time to fill to pool was that it was the total time. So the time would include the time taken for X and Y to fill the pool to half plus the time for Y (orX) to fill the other half.

Re: An empty swimming pool with a capacity of 75,000 liters is [#permalink]
02 Jun 2013, 04:47

Expert's post

timica wrote:

I was a bit confused with this question. My interpretation of the time to fill to pool was that it was the total time. So the time would include the time taken for X and Y to fill the pool to half plus the time for Y (orX) to fill the other half.

Timica

Consider this: the pool is to be filled by hoses X and Y simultaneously. The question is: how long, in hours, will it take to fill the pool? _________________

Re: An empty swimming pool with a capacity of 75,000 liters is [#permalink]
09 Sep 2013, 12:16

Hi ! I know I am way past the time for this thread but I'll still give my thoughts for someone coming here in the future!

I find DS questions easier to comprehend once I write down the data in a form of equation (s). IN the given questions, lets take the respective rates of hoses X & Y to be r_x & r_y and the total time to be 't'. We need to find 't' , where t=75000/(r_x + r_y)

Once we write down the above equation, it becomes very clear that we need to find r_x & r_y together to be able to find 't'. Hence, we need both statements (1) & (2) together to solve the above. Hence, option C.

Thank you again for this awesome series brunel! I'll be looking forward to all the other juicy questions coming up!! _________________

Re: An empty swimming pool with a capacity of 75,000 liters is [#permalink]
24 Sep 2013, 09:23

1

This post received KUDOS

Bunuel wrote:

timica wrote:

I was a bit confused with this question. My interpretation of the time to fill to pool was that it was the total time. So the time would include the time taken for X and Y to fill the pool to half plus the time for Y (orX) to fill the other half.

Timica

Consider this: the pool is to be filled by hoses X and Y simultaneously. The question is: how long, in hours, will it take to fill the pool?

Hi Bunuel! I too thought that 21 and 16 are total time and therefore wrote my equations as:- 1. 21 = [75k/2(x+y)] + [75k/2y] 2. 16 = [75k/2(x+y)] + [75k/2x] k=1000, x = X's rate and y = Y's rate. This way too C will be the answer.

An empty swimming pool with a capacity of 75,000 liters is to be filled by hoses X and Y simultaneously. If the amount of water flowing from each hose is independent of the amount flowing from the other hose, how long, in hours, will it take to fi ll the pool?

(1) If hose X stopped fi lling the pool after hoses X and Y had filled half the pool, it would take 21 hours to fi ll the pool. After hose X stops, hose Y continues filling the remaining half of the pool alone, and we are told that it needs 21 hours for that, hence to fill the whole pool it needs 21*2=42 hours. We know the rate of Y, though know nothing about the rate of X. Not sufficient.

(2) If hose Y stopped fi lling the pool after hoses X and Y had filled half the pool, it would take 16 hours to fi ll the pool. Reverse case: after hose Y stops, hose X continues filling the remaining half of the pool alone, and we are told that it needs 16 hours for that, hence to fill the whole pool it needs 16*2=32 hours. We know the rate of X, though know nothing about the rate of Y. Not sufficient.

(1)+(2) We know the rates of both hose X and Y, hence we can calculate the time they'll need to fi ll the pool of 75,000 liters. Sufficient.

Answer: C.

Bunuel, how is the question blindly giving us the rates of Y and X respectively in 1 and 2?

I interpreted (1) to say the following t1/x + (1/y)*(t1+t2) = 1 t1 + t2 = 21 t1 = the time it takes both x and y to fill half of the pool t1/x + 21/y = 1

An empty swimming pool with a capacity of 75,000 liters is to be filled by hoses X and Y simultaneously. If the amount of water flowing from each hose is independent of the amount flowing from the other hose, how long, in hours, will it take to fi ll the pool?

(1) If hose X stopped fi lling the pool after hoses X and Y had filled half the pool, it would take 21 hours to fi ll the pool. After hose X stops, hose Y continues filling the remaining half of the pool alone, and we are told that it needs 21 hours for that, hence to fill the whole pool it needs 21*2=42 hours. We know the rate of Y, though know nothing about the rate of X. Not sufficient.

(2) If hose Y stopped fi lling the pool after hoses X and Y had filled half the pool, it would take 16 hours to fi ll the pool. Reverse case: after hose Y stops, hose X continues filling the remaining half of the pool alone, and we are told that it needs 16 hours for that, hence to fill the whole pool it needs 16*2=32 hours. We know the rate of X, though know nothing about the rate of Y. Not sufficient.

(1)+(2) We know the rates of both hose X and Y, hence we can calculate the time they'll need to fi ll the pool of 75,000 liters. Sufficient.

Answer: C.

Bunuel, how is the question blindly giving us the rates of Y and X respectively in 1 and 2?

I interpreted (1) to say the following t1/x + (1/y)*(t1+t2) = 1 t1 + t2 = 21 t1 = the time it takes both x and y to fill half of the pool t1/x + 21/y = 1

Can you show me where I went wrong?

It should be \(t_1(\frac{1}{x}+\frac{1}{y}) + t_2(\frac{1}{y}) = 1\), where \(t_2=21\). We know that \(t_2(\frac{1}{y}) = \frac{1}{2}\), thus \(\frac{21}{y} = \frac{1}{2}\) --> \(y = 42\) hours. _________________

Re: An empty swimming pool with a capacity of 75,000 liters is [#permalink]
03 Aug 2014, 11:39

Bunuel wrote:

TooLong150 wrote:

Bunuel wrote:

An empty swimming pool with a capacity of 75,000 liters is to be filled by hoses X and Y simultaneously. If the amount of water flowing from each hose is independent of the amount flowing from the other hose, how long, in hours, will it take to fi ll the pool?

(1) If hose X stopped fi lling the pool after hoses X and Y had filled half the pool, it would take 21 hours to fi ll the pool. After hose X stops, hose Y continues filling the remaining half of the pool alone, and we are told that it needs 21 hours for that, hence to fill the whole pool it needs 21*2=42 hours. We know the rate of Y, though know nothing about the rate of X. Not sufficient.

(2) If hose Y stopped fi lling the pool after hoses X and Y had filled half the pool, it would take 16 hours to fi ll the pool. Reverse case: after hose Y stops, hose X continues filling the remaining half of the pool alone, and we are told that it needs 16 hours for that, hence to fill the whole pool it needs 16*2=32 hours. We know the rate of X, though know nothing about the rate of Y. Not sufficient.

(1)+(2) We know the rates of both hose X and Y, hence we can calculate the time they'll need to fi ll the pool of 75,000 liters. Sufficient.

Answer: C.

Bunuel, how is the question blindly giving us the rates of Y and X respectively in 1 and 2?

I interpreted (1) to say the following t1/x + (1/y)*(t1+t2) = 1 t1 + t2 = 21 t1 = the time it takes both x and y to fill half of the pool t1/x + 21/y = 1

Can you show me where I went wrong?

It should be \(t_1(\frac{1}{x}+\frac{1}{y}) + t_2(\frac{1}{y}) = 1\), where \(t_2=21\). We know that \(t_2(\frac{1}{y}) = \frac{1}{2}\), thus \(\frac{21}{y} = \frac{1}{2}\) --> \(y = 42\) hours.

I think that they mean that \(t_1 + t_2 = 21\) and not \(t_2=21\)

Re: An empty swimming pool with a capacity of 75,000 liters is [#permalink]
14 Aug 2014, 02:56

Bunuel wrote:

An empty swimming pool with a capacity of 75,000 liters is to be filled by hoses X and Y simultaneously. If the amount of water flowing from each hose is independent of the amount flowing from the other hose, how long, in hours, will it take to fi ll the pool?

(1) If hose X stopped fi lling the pool after hoses X and Y had filled half the pool, it would take 21 hours to fi ll the pool. After hose X stops, hose Y continues filling the remaining half of the pool alone, and we are told that it needs 21 hours for that, hence to fill the whole pool it needs 21*2=42 hours. We know the rate of Y, though know nothing about the rate of X. Not sufficient.

(2) If hose Y stopped fi lling the pool after hoses X and Y had filled half the pool, it would take 16 hours to fi ll the pool. Reverse case: after hose Y stops, hose X continues filling the remaining half of the pool alone, and we are told that it needs 16 hours for that, hence to fill the whole pool it needs 16*2=32 hours. We know the rate of X, though know nothing about the rate of Y. Not sufficient.

(1)+(2) We know the rates of both hose X and Y, hence we can calculate the time they'll need to fi ll the pool of 75,000 liters. Sufficient.

Answer: C.

I answered it incorrectly. My thought was: We know that first half was filled by both X and Y. and Y filled for 21 hrs. So, 75000/2 ltr was filled by both in first half and Y filled for 21 hrs. (total 42 hrs) we can check that how much liters can X fill in the first half of the tank!! _________________

KUDOS please!! If it helped. Warm Regards. Visit My Blog

gmatclubot

Re: An empty swimming pool with a capacity of 75,000 liters is
[#permalink]
14 Aug 2014, 02:56

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