Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

In a certain bathtub, both the hot and cold water fixtures [#permalink]

Show Tags

29 Jan 2010, 01:49

1

This post received KUDOS

10

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

95% (hard)

Question Stats:

44% (02:45) correct
56% (01:28) wrong based on 318 sessions

HideShow timer Statistics

In a certain bathtub, both the hot and cold water fixtures leak. The cold water leak alone would fill an empty bucket in c hours, and the hot water leak alone will fill the same bucket in h hours, where c < h. If both fixtures began to leak at the same time into the empty bucket at their respective constant rates and consequently it tool t hours to fill the bucket, which of the following must be true?

I. 0 < t < h II. c < t <h III. c/2 < t < h/2

A. I only B. II only C. III only D. I and II E. I and III

Re: GMAT Prep2 - Time and Work Problem.Please help [#permalink]

Show Tags

01 Feb 2010, 13:23

I think OA is 1 (I Only) Reason: Both condition 2 and 3 imply that c< h which is opposite to the problem statement. 1 is correct because t will be always less than either c or h by itself (sum of flow rates always grater than an individual flow rate) and will be greater than zero, as time that takes to fill up the bath tab has to be positive number.

Re: GMAT Prep2 - Time and Work Problem.Please help [#permalink]

Show Tags

01 Feb 2010, 17:32

The answer is 5.

I is always true since the T value of C+H will always be smaller than H alone.

II may not always be true as it is dependent on the values for C & H.

III is always true given the fact that C > H.

Sanjay already did the math for the last part to prove that the result of C + H < 2C must always be true.

I took the algebra-free approach. Given it takes C less time to fill the tub than it does H, then you know that C/2 is less than H/2. Additionally, the two working together (C+H) would have to be somewhere between the two due to their unequal rates of flow.

Re: GMAT Prep2 - Time and Work Problem.Please help [#permalink]

Show Tags

02 Feb 2010, 06:19

LJ wrote:

The answer is 5.

I is always true since the T value of C+H will always be smaller than H alone.

II may not always be true as it is dependent on the values for C & H.

III is always true given the fact that C > H.

Sanjay already did the math for the last part to prove that the result of C + H < 2C must always be true.

I took the algebra-free approach. Given it takes C less time to fill the tub than it does H, then you know that C/2 is less than H/2. Additionally, the two working together (C+H) would have to be somewhere between the two due to their unequal rates of flow.

How can c/2 < h/2, while we have c>h, and we are talking about positive whole numbers? Please explain.

Re: GMAT Prep2 - Time and Work Problem.Please help [#permalink]

Show Tags

03 Feb 2010, 18:42

alexBLR wrote:

LJ wrote:

The answer is 5.

I is always true since the T value of C+H will always be smaller than H alone.

II may not always be true as it is dependent on the values for C & H.

III is always true given the fact that C > H.

Sanjay already did the math for the last part to prove that the result of C + H < 2C must always be true.

I took the algebra-free approach. Given it takes C less time to fill the tub than it does H, then you know that C/2 is less than H/2. Additionally, the two working together (C+H) would have to be somewhere between the two due to their unequal rates of flow.

How can c/2 < h/2, while we have c>h, and we are talking about positive whole numbers? Please explain.

I see the way I wrote it could be confusing.

C/2 would be described as half the time it takes C to fill the tub alone. H/2 would be described as half the time it takes H to fill the tub alone. T, aka (H + C) is the time it takes for the faucets to fill the tub together.

Since C alone fills the tub faster than H, you can see that C working twice as fast (C/2) would fill the tub faster than H+C, therefore it is less than T. The opposite is true for H.

Re: GMAT Prep2 - Time and Work Problem.Please help [#permalink]

Show Tags

04 Feb 2010, 06:16

6

This post received KUDOS

Expert's post

5

This post was BOOKMARKED

In a certain bathtub, both the hot and cold water fixtures leak.The cold water leak alone would fill an empty bucket in \(c\) hours, and the hot water leak alone will fill the same bucket in \(h\) hours, where \(c>h\). If both fixtures began to leak at the same time into the empty bucket at their respective constant rates and consequently it tool \(t\) hours to fill the bucket, which of the following must be true?

1. 0 < t < h 2. c < t <h 3. c/2 < t < h/2

(A) I only (B) II only (C) III only (D) I and II (E) I and III

There is NO WAY (E) can be the correct answer. The answer for the question above must be (A) I only.

Given \(c>h\): 2. is never correct as \(c < t <h\), means \(c<h\) and that contradicts the stem;

3. is never correct as \(\frac{c}{2}<t<\frac{h}{2}\), means \(\frac{c}{2}<\frac{h}{2}\) or \(c<h\) and that contradicts the stem.

1. is always correct, as time needed for both fixtures leaking (working) together to fill the bucket, \(t\), must always be less than time needed for either of fixture leaking (working) alone to fill the bucket.

Guess the original question had \(c<h\) (not \(c>h\)). In this case yes E is the correct answer.

1. remains correct as explained above.

2. can not be correct: \(t\), time needed for both fixtures leaking (working) together to fill the bucket, must always be less than time needed for either of fixture leaking (working) alone to fill the bucket. So \(c<t\) not true.

3. To prove that this is always correct we can use pure logic or algebra.

Logic: If both fixtures were leaking at identical rate then c/2=h/2=t but as the rate of cold water is higher (because it needs less time) then c/2<t and as the rate of hot water is lower then t<h/2.

Algebraic approach would be:

Given: \(c<h\) and \(t=\frac{ch}{c+h}\)

\(\frac{c}{2}<\frac{ch}{c+h}<\frac{h}{2}\)? break down: \(\frac{c}{2}<\frac{ch}{c+h}\)? and \(\frac{ch}{c+h}<\frac{h}{2}\)?

\(\frac{c}{2}<\frac{ch}{c+h}\)? --> \(c^2+ch< 2ch\)? --> \(c^2<ch\)? --> \(c<h\)? Now, this is given to be true.

\(\frac{ch}{c+h}<\frac{h}{2}\)? --> \(2ch<ch+h^2\)? --> \(ch<h^2\)? --> \(c<h\)? Now, this is given to be true.

So 3 is also always true. Answer E (in case we change the stem).

Very tricky problem. The math itself requires some insight, then they stick it to you with an inequalities and wording trick!

The cold faucet rate is 1 bucket in c hours = 1/c (buckets per hour) The hot faucet rate is 1 bucket in h hours = 1/h (buckets per hour)

The combined rate can be computed as the sum of the individual rates = [1/c + 1/h] (buckets per hour). The combined rate is also given to us directly as 1 bucket in t hours = 1/t (buckets per hour).

Relating t to c and h: [1/c + 1/h] = 1/t [(h+c)/ch] = 1/t t = ch/(h+c)

Seeing that all the answers had inequalities, and that c<h was given, I wrote the following on paper:

t = c*c'/(c'+c), where the mark (') indicates "a little more than." t = (c^2)'/(2c)' = (c/2)'

t = h"*h/(h + h"), where the mark (") indicates "a little less than." t = (h^2)"/(2h)" = (h/2)"

Put it together: c/2 < t < h/2, which corresponds to III directly.

But the final trick is that since c is positive (i.e. the cold faucet leak doesn't fill the bucket in literally no time.), 0< c/2 < t. Since h is positive (same reason), h > h/2 > t.

Put all that together: 0 < c/2 < t < h/2 < h 0 < t < h, so I also "must be true." _________________

Emily Sledge | Manhattan GMAT Instructor | St. Louis

Very tricky problem. The math itself requires some insight, then they stick it to you with an inequalities and wording trick!

The cold faucet rate is 1 bucket in c hours = 1/c (buckets per hour) The hot faucet rate is 1 bucket in h hours = 1/h (buckets per hour)

The combined rate can be computed as the sum of the individual rates = [1/c + 1/h] (buckets per hour). The combined rate is also given to us directly as 1 bucket in t hours = 1/t (buckets per hour).

Relating t to c and h: [1/c + 1/h] = 1/t [(h+c)/ch] = 1/t t = ch/(h+c)

Seeing that all the answers had inequalities, and that c<h was given, I wrote the following on paper:

t = c*c'/(c'+c), where the mark (') indicates "a little more than." t = (c^2)'/(2c)' = (c/2)'

t = h"*h/(h + h"), where the mark (") indicates "a little less than." t = (h^2)"/(2h)" = (h/2)"

Put it together: c/2 < t < h/2, which corresponds to III directly.

But the final trick is that since c is positive (i.e. the cold faucet leak doesn't fill the bucket in literally no time.), 0< c/2 < t. Since h is positive (same reason), h > h/2 > t.

Put all that together: 0 < c/2 < t < h/2 < h 0 < t < h, so I also "must be true."

Once you have found the value of t=ch/c+h, Try plugging in the values of t in choices:

(1) 0 < t < h

0<ch/c+h<h we get c>0 true & c<c+h also true hence Chose 1 is correct.

(2) c < t < h

c<ch/c+h<h, we get c+h<h (from solving the L.H.S of the inequality) - False & c<c+h (from solving the R.H.S of the inequality) - True - Hence Choice 2 is incorrect.

(3) (c/2) < t < (h/2)

c/2<ch/c+h<h/2, we get c<h (from solving the L.H.S of the inequality) - True & c<h (from solving the R.H.S of the inequality) - True - Hence Choice 3 is incorrect.

Re: In a certain bathtub,both the hot and cold water fixtures [#permalink]

Show Tags

02 Sep 2012, 13:17

1

This post received KUDOS

Question asked is "which option MUST BE true", so if i can prove any option wrong , i can easily select the correct answer. So i preferred to use value for these variables as i am trying to prove few options are incorrect As c>h let c = 4 hrs h = 2 hrs Thus t = 8/6 = 4/3 hr

Now if put these value only option A is true

Thus as per me the answer has to be A _________________

If you like my Question/Explanation or the contribution, Kindly appreciate by pressing KUDOS. Kudos always maximizes GMATCLUB worth-Game Theory

If you have any question regarding my post, kindly pm me or else I won't be able to reply

Re: In a certain bathtub,both the hot and cold water fixtures [#permalink]

Show Tags

21 Feb 2013, 22:37

The original posted stem says c>h. In which case E can not be the answer, only A. In the correct version (posted later) the stem says c<h. In this case E is the answer. Can someone please change the original posted stem to match the question they were trying to copy in order to clear up the confusion.

Re: In a certain bathtub,both the hot and cold water fixtures [#permalink]

Show Tags

22 Feb 2013, 01:51

Expert's post

coreyrnichols wrote:

The original posted stem says c>h. In which case E can not be the answer, only A. In the correct version (posted later) the stem says c<h. In this case E is the answer. Can someone please change the original posted stem to match the question they were trying to copy in order to clear up the confusion.

Edited the question and added OA. _________________

Re: In a certain bathtub, both the hot and cold water fixtures [#permalink]

Show Tags

19 Sep 2014, 13:50

Hello from the GMAT Club BumpBot!

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: In a certain bathtub, both the hot and cold water fixtures [#permalink]

Show Tags

08 May 2016, 04:42

Hello from the GMAT Club BumpBot!

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. _________________

http://blog.ryandumlao.com/wp-content/uploads/2016/05/IMG_20130807_232118.jpg The GMAT is the biggest point of worry for most aspiring applicants, and with good reason. It’s another standardized test when most of us...

I recently returned from attending the London Business School Admits Weekend held last week. Let me just say upfront - for those who are planning to apply for the...