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A bathtub has two faucets, P and Q, and one drain. Faucet P [#permalink]
15 Nov 2010, 10:39

5

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

85% (hard)

Question Stats:

57% (03:32) correct
43% (02:07) wrong based on 157 sessions

A bathtub has two faucets, P and Q, and one drain. Faucet P alone can fill the whole tub in ten minutes, and faucet Q alone can fill the whole tub four minutes faster than the drain can empty the whole tub. With faucets P and Q both running and the drain unstopped, the tub fills in six minutes. How long would the drain take to empty the whole tub?

A bathtub has two faucets, P and Q, and one drain. Faucet P alone can fill the whole tub in ten minutes, and faucet Q alone can fill the whole tub four minutes faster than the drain can empty the whole tub. With faucets P and Q both running and the drain unstopped, the tub fills in six minutes. How long would the drain take to empty the whole tub?

Don't know why this question didn't get any attention. It is a great example of using options to your advantage in GMAT.

Time taken by faucet P to fill the tub alone = 10 mins so rate of P = 1/10 Time taken by drain to empty the tub = r min so rate of drain = -1/r (Since the drain removes water, it does negative work) Time taken by faucet Q to fill the tub alone = r - 4 min so rate of Q = 1/(r - 4)

All 3 working together fill the tub in 6 mins. I get: \frac{1}{10} + \frac{1}{{r-4}} - \frac{1}{r} = \frac{1}{6}

A quick look at the options tells me that if r = 10, r - 4 = 6 and the equation looks like this \frac{1}{10} + \frac{1}{6} - \frac{1}{10} = \frac{1}{6} Since r = 10 satisfies the equation, answer is 10 minutes. Option (C). (Of course you could have solved the quadratic to get r = 10 as well though it would have taken more time.)

In fact putting into rate and equations is also a lot of work. When I read the question, I said to myself, P takes 10 min, Q takes 4 mins less than the drain takes to empty. All working together, take 6 mins and I sneak peeked at the options. What caught my fancy immediately was 6 and 10 in options... and suddenly the answer became clear. P takes 10 min to fill the tub alone, the drain takes 10 mins to empty it. So whatever P pumps in the tub, drain takes out. In effect, Q is the only one working and since it will take 4 mins less to fill the tub, it takes 6 min and that is why the time taken by all 3 together is 6 mins.

Remember, in GMAT, once you filter out the logic, the numbers always fall beautifully in place. Someone once told me, if you did long calculations in GMAT, it is as if you were at comedy central and didn't get the joke while everyone else around you was laughing... _________________

A bathtub has two faucets, P and Q, and one drain. Faucet P [#permalink]
06 Dec 2010, 04:02

A bathtub has two faucets, P and Q, and one drain. Faucet P alone can fill the whole tub in ten minutes, and faucet Q alone can fill the whole tub four minutes faster than the drain can empty the whole tub. With faucets P and Q both running and the drain unstopped, the tub fills in six minutes. How long would the drain take to empty the whole tub?

Re: MGMAT Challenge Test 1 #16 [#permalink]
06 Dec 2010, 04:15

4

This post received KUDOS

Expert's post

mmcooley33 wrote:

A bathtub has two faucets, P and Q, and one drain. Faucet P alone can fill the whole tub in ten minutes, and faucet Q alone can fill the whole tub four minutes faster than the drain can empty the whole tub. With faucets P and Q both running and the drain unstopped, the tub fills in six minutes. How long would the drain take to empty the whole tub?

I solved the current problem by setting up 1/10 + 1/(d-4)=1/6

6(d-4)/60(d-4) + 60/60(d+4) = 10(d+4)/60(d+4)

6d - 24 +60 = 10d -40 76=4d d=19 where D= drain time, I was wondering if that is a correct method or was I just lucky with the answer being what it was?

I doubt that answer D is correct here. Stem says that "...faucets P and Q both running and the drain unstopped..." so you should subtract the rate of drain per minute 1/d from 1/10 + 1/(d-4).

Complete solution:

Let p and q be the times in minutes needed for faucets P and Q working alone to fill the tub and d be the time in minutes needed for drain to empty the tub.

Given: Faucet P alone can fill the whole tub in ten minutes --> p=10; Faucet Q alone can fill the whole tub four minutes faster than the drain can empty the whole tub --> q=d-4; Faucets P and Q both running and the drain unstopped, the tub fills in six minutes --> \frac{1}{p}+\frac{1}{q}-\frac{1}{d}=\frac{1}{6} --> \frac{1}{10}+\frac{1}{d-4}-\frac{1}{d}=\frac{1}{6} --> \frac{1}{d-4}-\frac{1}{d}=\frac{1}{15} --> substituting the values from the answer choices we'll get d=10.

A bathtub has two faucets, P and Q, and one drain. Faucet P alone can fill the whole tub in ten minutes, and faucet Q alone can fill the whole tub four minutes faster than the drain can empty the whole tub. With faucets P and Q both running and the drain unstopped, the tub fills in six minutes. How long would the drain take to empty the whole tub?

Don't know why this question didn't get any attention. It is a great example of using options to your advantage in GMAT.

Time taken by faucet P to fill the tub alone = 10 mins so rate of P = 1/10 Time taken by drain to empty the tub = r min so rate of drain = -1/r (Since the drain removes water, it does negative work) Time taken by faucet Q to fill the tub alone = r - 4 min so rate of Q = 1/(r - 4)

All 3 working together fill the tub in 6 mins. I get: \frac{1}{10} + \frac{1}{{r-4}} - \frac{1}{r} = \frac{1}{6}

A quick look at the options tells me that if r = 10, r - 4 = 6 and the equation looks like this \frac{1}{10} + \frac{1}{6} - \frac{1}{10} = \frac{1}{6} Since r = 10 satisfies the equation, answer is 10 minutes. Option (C). (Of course you could have solved the quadratic to get r = 10 as well though it would have taken more time.)

In fact putting into rate and equations is also a lot of work. When I read the question, I said to myself, P takes 10 min, Q takes 4 mins less than the drain takes to empty. All working together, take 6 mins and I sneak peeked at the options. What caught my fancy immediately was 6 and 10 in options... and suddenly the answer became clear. P takes 10 min to fill the tub alone, the drain takes 10 mins to empty it. So whatever P pumps in the tub, drain takes out. In effect, Q is the only one working and since it will take 4 mins less to fill the tub, it takes 6 min and that is why the time taken by all 3 together is 6 mins.

Remember, in GMAT, once you filter out the logic, the numbers always fall beautifully in place. Someone once told me, if you did long calculations in GMAT, it is as if you were at comedy central and didn't get the joke while everyone else around you was laughing...

Building on what you said about numbers beautifully falling into place in GMAT, we can see that most of the time when we encounter equations as the one in this question, its almost always a case of quick and easy factorization rather than trying to solve a quadratic equation.

For e.g., here, the equation quickly reduces to (r)*(r-4) = 60, so we need to factor 60 into two factors that are 4 apart, and obvious choice would be 10 and 6, so answer is 10. You really don't need to go down the quadratic route in most cases.

Re: A bathtub has two faucets, P and Q, and one drain. Faucet P [#permalink]
09 Nov 2012, 00:01

Pansi wrote:

A bathtub has two faucets, P and Q, and one drain. Faucet P alone can fill the whole tub in ten minutes, and faucet Q alone can fill the whole tub four minutes faster than the drain can empty the whole tub. With faucets P and Q both running and the drain unstopped, the tub fills in six minutes. How long would the drain take to empty the whole tub?

Re: A bathtub has two faucets, P and Q, and one drain. Faucet P [#permalink]
09 Nov 2012, 02:15

Vips0000 wrote:

Pansi wrote:

A bathtub has two faucets, P and Q, and one drain. Faucet P alone can fill the whole tub in ten minutes, and faucet Q alone can fill the whole tub four minutes faster than the drain can empty the whole tub. With faucets P and Q both running and the drain unstopped, the tub fills in six minutes. How long would the drain take to empty the whole tub?

Let's substitute the answer choices for variable D: A) Crazy looking value so I skipped B) \frac{1}{2}-\frac{1}{6}=\frac{1}{3} This is not the one! C) \frac{1}{6}-\frac{1}{10}=4/60 Bingo! _________________

A bathtub has two faucets, P and Q, and one drain. Faucet P alone can fill the whole tub in ten minutes, and faucet Q alone can fill the whole tub four minutes faster than the drain can empty the whole tub. With faucets P and Q both running and the drain unstopped, the tub fills in six minutes. How long would the drain take to empty the whole tub?

I solved the current problem by setting up 1/10 + 1/(d-4)=1/6

6(d-4)/60(d-4) + 60/60(d+4) = 10(d+4)/60(d+4)

6d - 24 +60 = 10d -40 76=4d d=19 where D= drain time, I was wondering if that is a correct method or was I just lucky with the answer being what it was?

I doubt that answer D is correct here. Stem says that "...faucets P and Q both running and the drain unstopped..." so you should subtract the rate of drain per minute 1/d from 1/10 + 1/(d-4).

Complete solution:

Let p and q be the times in minutes needed for faucets P and Q working alone to fill the tub and d be the time in minutes needed for drain to empty the tub.

Given: Faucet P alone can fill the whole tub in ten minutes --> p=10; Faucet Q alone can fill the whole tub four minutes faster than the drain can empty the whole tub --> q=d-4; Faucets P and Q both running and the drain unstopped, the tub fills in six minutes --> \frac{1}{p}+\frac{1}{q}-\frac{1}{d}=\frac{1}{6} --> \frac{1}{10}+\frac{1}{d-4}-\frac{1}{d}=\frac{1}{6} --> \frac{1}{d-4}-\frac{1}{d}=\frac{1}{15} --> substituting the values from the answer choices we'll get d=10.

A bathtub has two faucets, P and Q, and one drain. Faucet P alone can fill the whole tub in ten minutes, and faucet Q alone can fill the whole tub four minutes faster than the drain can empty the whole tub. With faucets P and Q both running and the drain unstopped, the tub fills in six minutes. How long would the drain take to empty the whole tub?

I solved the current problem by setting up 1/10 + 1/(d-4)=1/6

6(d-4)/60(d-4) + 60/60(d+4) = 10(d+4)/60(d+4)

6d - 24 +60 = 10d -40 76=4d d=19 where D= drain time, I was wondering if that is a correct method or was I just lucky with the answer being what it was?

I doubt that answer D is correct here. Stem says that "...faucets P and Q both running and the drain unstopped..." so you should subtract the rate of drain per minute 1/d from 1/10 + 1/(d-4).

Complete solution:

Let p and q be the times in minutes needed for faucets P and Q working alone to fill the tub and d be the time in minutes needed for drain to empty the tub.

Given: Faucet P alone can fill the whole tub in ten minutes --> p=10; Faucet Q alone can fill the whole tub four minutes faster than the drain can empty the whole tub --> q=d-4; Faucets P and Q both running and the drain unstopped, the tub fills in six minutes --> \frac{1}{p}+\frac{1}{q}-\frac{1}{d}=\frac{1}{6} --> \frac{1}{10}+\frac{1}{d-4}-\frac{1}{d}=\frac{1}{6} --> \frac{1}{d-4}-\frac{1}{d}=\frac{1}{15} --> substituting the values from the answer choices we'll get d=10.

Re: A bathtub has two faucets, P and Q, and one drain. Faucet P [#permalink]
31 Jul 2013, 11:27

Hey Bunuel, when you get to the final equation, would you recommend running out the quadratic and solving for d=10 that way, or would you recommend plugging in the answer choices? I'm sure you can do the quadratic element in about three seconds in your head from the fractions, but for us mere mortals, what would make us choose one over the other?

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________

Re: A bathtub has two faucets, P and Q, and one drain. Faucet P [#permalink]
19 Jan 2014, 07:29

mrinal2100 wrote:

A bathtub has two faucets, P and Q, and one drain. Faucet P alone can fill the whole tub in ten minutes, and faucet Q alone can fill the whole tub four minutes faster than the drain can empty the whole tub. With faucets P and Q both running and the drain unstopped, the tub fills in six minutes. How long would the drain take to empty the whole tub?

lets take the easiest option to verify: Option B) 6 mins P takes 10 mins. Drain - 6, Q should take 2 mins If 30 is total amount of work done (LCM of 10, 6, 2) P does = 30/10 = 3, Drain = 5, Q = 15 P+Q-Drain = 13. Now 30/13 is not 6, next option

Option C) P = 10 mins, Drain = 10 mins, Q = 6 mins LCM = 30 P does = 3, Drain = 3, Q does = 5 So P+Q-Drain = 5 30/ 5 = 6 mins BINGO !!! _________________