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mrinal2100
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A bathtub has two faucets, P and Q, and one drain. Faucet P 15 Nov 2010, 11:39
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

75% (hard)

Question Stats:

65% (02:49) correct 35% (03:01) wrong based on 911 sessions

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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) 5 (5/11) minutes
(B) 6 minutes
(C) 10 minutes
(D) 19 minutes
(E) 30 minutes
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C
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A bathtub has two faucets, P and Q, and one drain. Faucet P 18 Nov 2010, 19:49
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mrinal2100
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) 5 (5/11) minutes
(B) 6 minutes
(C) 10 minutes
(D) 19 minutes
(E) 30 minutes
Show more

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...
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A bathtub has two faucets, P and Q, and one drain. Faucet P 06 Dec 2010, 05:15
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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?


5 and 5/11 minutes
6 minutes
10 minutes
19 minutes
30 minutes

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?
Show more

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 \(d=10\).

Answer: C.

Check this for theory on work problems:
word-translations-rates-work-104208.html?hilit=printer#p812628

Hope it helps.
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A bathtub has two faucets, P and Q, and one drain. Faucet P 21 Nov 2010, 13:51
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Took 10 secs to analyze what it meant by "drain unstopped", which i thought when it's not getting drained.

In 1 min- P fills- 1/10
in 1 min- drain fills- 1/d
thus,
in 1 min- Q fills- 1/(d-4)

1/10 + 1/(d-4) = total tub fill in 1 min

Thus in 6 mins-

(1/10 + 1/(d-4)) * 6 = 1

Solving above- d=19 minutes

Answer:-D
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A bathtub has two faucets, P and Q, and one drain. Faucet P 21 Nov 2010, 13:55
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When I do consider "drain unstopped" as it's getting drained simulteneously, the answer changes to 10

Answer:- C


Bottom line- need to pay close attention to GMAT question wordings...
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A bathtub has two faucets, P and Q, and one drain. Faucet P Updated on: 09 Nov 2012, 02:20
Originally posted by mmcooley33 on 06 Dec 2010, 05:02.
Last edited by Bunuel on 09 Nov 2012, 02:20, edited 2 times in total.
Edited the OA.
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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) 5 (5/11) minutes
(B) 6 minutes
(C) 10 minutes
(D) 19 minutes
(E) 30 minutes
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A bathtub has two faucets, P and Q, and one drain. Faucet P 06 Dec 2010, 05:21
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my bad you are correct, im a little strung out. OA is C, and thanks for the help!
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A bathtub has two faucets, P and Q, and one drain. Faucet P 07 Mar 2011, 03:22
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VeritasPrepKarishma
mrinal2100
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) 5 (5/11) minutes
(B) 6 minutes
(C) 10 minutes
(D) 19 minutes
(E) 30 minutes

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...
Show more

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.
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A bathtub has two faucets, P and Q, and one drain. Faucet P 09 Nov 2012, 01:01
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Pansi
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) 5 (5/11) minutes
(B) 6 minutes
(C) 10 minutes
(D) 19 minutes
(E) 30 minutes
Show more

1/10 + 1/(R+4)- 1/R = 1/6 => R=10

Ans C it is.
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A bathtub has two faucets, P and Q, and one drain. Faucet P 09 Nov 2012, 03:15
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Vips0000
Pansi
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) 5 (5/11) minutes
(B) 6 minutes
(C) 10 minutes
(D) 19 minutes
(E) 30 minutes

1/10 + 1/(R+4)- 1/R = 1/6 => R=10

Ans C it is.
Show more

Vips, I believe it should be 1/10 + 1/(R-4)- 1/R = 1/6 => R=10
(R-4), not (R+4)
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A bathtub has two faucets, P and Q, and one drain. Faucet P 14 Nov 2012, 02:23
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\(\frac{1}{10}+\frac{1}{D-4}-\frac{1}{D}=\frac{1}{6}\)
\(\frac{1}{D-4}-\frac{1}{D}=4/60\)

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!
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A bathtub has two faucets, P and Q, and one drain. Faucet P 30 Jul 2013, 19:34
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Bunuel
mmcooley33
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?


5 and 5/11 minutes
6 minutes
10 minutes
19 minutes
30 minutes

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 \(d=10\).

Answer: C.

Check this for theory on work problems:
word-translations-rates-work-104208.html?hilit=printer#p812628

Hope it helps.
Show more

Why is q = d-4 instead of d+4?

The time is more 4 minutes more than the drainage time. If the drain times is d, why is q = d+4 incorrect?

Thanx
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A bathtub has two faucets, P and Q, and one drain. Faucet P 31 Jul 2013, 00:52
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mmcooley33
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?


5 and 5/11 minutes
6 minutes
10 minutes
19 minutes
30 minutes

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 \(d=10\).

Answer: C.

Check this for theory on work problems:
word-translations-rates-work-104208.html?hilit=printer#p812628

Hope it helps.

Why is q = d-4 instead of d+4?

The time is more 4 minutes more than the drainage time. If the drain times is d, why is q = d+4 incorrect?

Thanx
Show more

Faucet Q alone can fill the whole tub four minutes faster than the drain can empty the whole tub --> q is 4 less than d --> q=d-4.

Hope it's clear.
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A bathtub has two faucets, P and Q, and one drain. Faucet P 31 Jul 2013, 12:27
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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!
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A bathtub has two faucets, P and Q, and one drain. Faucet P 05 Oct 2013, 03:57
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Merging similar topics.
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A bathtub has two faucets, P and Q, and one drain. Faucet P 19 Jan 2014, 08:29
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mrinal2100
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) 5 (5/11) minutes
(B) 6 minutes
(C) 10 minutes
(D) 19 minutes
(E) 30 minutes
Show more

Use Options.

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 !!!
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A bathtub has two faucets, P and Q, and one drain. Faucet P 08 Mar 2015, 05:18
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A good question in which the only way we can go wrong is by missing the word :UNSTOPPED.

Good one!!!
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A bathtub has two faucets, P and Q, and one drain. Faucet P 23 Apr 2018, 17:39
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mrinal2100
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) 5 (5/11) minutes
(B) 6 minutes
(C) 10 minutes
(D) 19 minutes
(E) 30 minutes
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Let’s let n = the time it takes the drain to empty the tub. The fill rate of faucet P is 1/10, the fill rate of faucet P is 1/(n - 4), and the drain rate of the drain is 1/n. We see that with both faucets running and the drain unstopped, the tub fills in 6 minutes. Thus, we know that the sum of the fill rates of P and Q, less the “emptying rate” of the drain, yields a full tub in 6 minutes. We can create the equation that describes this activity as:,
1/10 + 1/(n-4) - 1/n = 1/6

We can multiply the entire equation by 30n(n-4) and we have:

3n(n-4) + 30n - 30(n-4) = 5n(n-4)

3n^2 - 12n + 30n - 30n + 120 = 5n^2 - 20n

2n^2 - 8n - 120 = 0

n^2 - 4n - 60 = 0

(n - 10)(n + 6) = 0

n = 10 or n = -6

Since n must be positive, n = 10. This means that if the tub were full of water, and neither P nor Q was operating at all, then it would take 10 minutes for the entire tub to drain.

Answer: C
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A bathtub has two faucets, P and Q, and one drain. Faucet P 26 Oct 2020, 01:29
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VeritasKarishma
mrinal2100
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) 5 (5/11) minutes
(B) 6 minutes
(C) 10 minutes
(D) 19 minutes
(E) 30 minutes

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...
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Hi Karishma. Thanks for this splendid explanation!

A bit out-of-topic question here. Given that rate = (1/time), reciprocally, can we safely say that time = (1/rate) ?
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A bathtub has two faucets, P and Q, and one drain. Faucet P 28 Oct 2020, 00:33
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tagheueraquaracer
VeritasKarishma
mrinal2100
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) 5 (5/11) minutes
(B) 6 minutes
(C) 10 minutes
(D) 19 minutes
(E) 30 minutes

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...

Hi Karishma. Thanks for this splendid explanation!

A bit out-of-topic question here. Given that rate = (1/time), reciprocally, can we safely say that time = (1/rate) ?
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tagheueraquaracer

Yes, when work done = 1, then rate = 1/time and time = 1/rate.
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