GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 24 Sep 2018, 15:07

Close

GMAT Club Daily Prep

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.

Close

Request Expert Reply

Confirm Cancel

In a certain bathtub, both the hot and cold water fixtures

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Intern
Intern
avatar
Joined: 04 Dec 2009
Posts: 19
In a certain bathtub, both the hot and cold water fixtures  [#permalink]

Show Tags

New post Updated on: 22 Feb 2013, 01:49
1
15
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

55% (02:21) correct 45% (02:23) wrong based on 447 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

Originally posted by gautamsubrahmanyam on 29 Jan 2010, 01:49.
Last edited by Bunuel on 22 Feb 2013, 01:49, edited 1 time in total.
Edited the question and added OA.
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49430
Re: GMAT Prep2 - Time and Work Problem.Please help  [#permalink]

Show Tags

New post 04 Feb 2010, 06:16
8
4
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).

Hope it's clear.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

General Discussion
Intern
Intern
User avatar
Joined: 31 Oct 2009
Posts: 27
Location: india
Schools: ISB hydrabad, IIMs
WE 1: Steel Authority of India Limited
Re: GMAT Prep2 - Time and Work Problem.Please help  [#permalink]

Show Tags

New post 29 Jan 2010, 03:44
2
Answer is 5

If both fixtures leak then it take to fill the bucket in t time which will be less than the time taken by any of fixture.
so, 1 is right

so 2 may not be right.

3 is also right

t=ch/(c+h)

doing back calculation

as 3 say

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

h/2<t
=> h/2< [ch/(c+h)]
=> c+h<2c
=>h<c which is right as per question
similarly we can prove that t<c/2

so iii is also correct
_________________

kumar sanjay
http://sanjay80.blogspot.com
9437488107

Manager
Manager
avatar
Joined: 17 Jan 2010
Posts: 137
Concentration: General Management, Strategy
GPA: 3.78
WE: Engineering (Manufacturing)
Re: GMAT Prep2 - Time and Work Problem.Please help  [#permalink]

Show Tags

New post 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.
Intern
Intern
User avatar
Status: Getting ready for the internship summer
Joined: 07 Jun 2009
Posts: 46
Location: Rochester, NY
Schools: Simon
WE 1: JPM - Treasury
Re: GMAT Prep2 - Time and Work Problem.Please help  [#permalink]

Show Tags

New post 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.
Director
Director
User avatar
Joined: 03 Sep 2006
Posts: 833
GMAT ToolKit User
Re: GMAT Prep2 - Time and Work Problem.Please help  [#permalink]

Show Tags

New post 01 Feb 2010, 21:51
(c x h)/ (c + h) = t

c > h

Thus by putting C = 1hr and h = 2hr

clearly (i) and (ii) are correct. Therefore only answer choice which seems possible is (4)
Manager
Manager
avatar
Joined: 17 Jan 2010
Posts: 137
Concentration: General Management, Strategy
GPA: 3.78
WE: Engineering (Manufacturing)
Re: GMAT Prep2 - Time and Work Problem.Please help  [#permalink]

Show Tags

New post 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.
Intern
Intern
User avatar
Status: Getting ready for the internship summer
Joined: 07 Jun 2009
Posts: 46
Location: Rochester, NY
Schools: Simon
WE 1: JPM - Treasury
Re: GMAT Prep2 - Time and Work Problem.Please help  [#permalink]

Show Tags

New post 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.
Manager
Manager
avatar
Joined: 13 Aug 2009
Posts: 134
WE 1: 4 years in IT
Gmat prep ps2  [#permalink]

Show Tags

New post 28 Mar 2010, 11:01
OA--E

Attachments

Gprep-ps-2.JPG
Gprep-ps-2.JPG [ 52.72 KiB | Viewed 7923 times ]

Manhattan Prep Instructor
User avatar
Joined: 28 Aug 2009
Posts: 152
Location: St. Louis, MO
Schools: Cornell (Bach. of Sci.), UCLA Anderson (MBA)
Re: Gmat prep ps2  [#permalink]

Show Tags

New post 28 Mar 2010, 12:04
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

Manhattan GMAT Discount | Manhattan GMAT Course Reviews | Manhattan GMAT Reviews

Intern
Intern
avatar
B
Joined: 28 Dec 2010
Posts: 23
Re: Gmat prep ps2  [#permalink]

Show Tags

New post 27 Feb 2011, 23:23
esledge wrote:
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.

Therefore, Choice 5 is the correct Answer.
Senior Manager
Senior Manager
avatar
B
Joined: 24 Aug 2009
Posts: 476
Schools: Harvard, Columbia, Stern, Booth, LSB,
Re: In a certain bathtub,both the hot and cold water fixtures  [#permalink]

Show Tags

New post 02 Sep 2012, 13:17
1
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

Senior Manager
Senior Manager
User avatar
Joined: 13 Aug 2012
Posts: 436
Concentration: Marketing, Finance
GPA: 3.23
GMAT ToolKit User
Re: In a certain bathtub,both the hot and cold water fixtures  [#permalink]

Show Tags

New post 14 Nov 2012, 06:33
1
Let c = 4
Let h = 5
\(\frac{1}{c}+\frac{1}{h}=\frac{1}{t}\)
\(\frac{1}{4}+\frac{1}{5}=\frac{9}{20}\)


I. 0 < \(\frac{20}{9}\) < 5 TRUE
II. 4 < \(\frac{20}{9}\) < 5 FALSE
III. 2 < 20/9 < 5/2 TRUE!

Answer: E
_________________

Impossible is nothing to God.

Intern
Intern
avatar
Joined: 08 Dec 2012
Posts: 7
Location: United States
Concentration: Finance, Strategy
GMAT 1: 760 Q48 V48
GPA: 3.71
WE: Sales (Energy and Utilities)
Re: In a certain bathtub,both the hot and cold water fixtures  [#permalink]

Show Tags

New post 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.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49430
Re: In a certain bathtub,both the hot and cold water fixtures  [#permalink]

Show Tags

New post 22 Feb 2013, 01:51
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.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Director
Director
User avatar
B
Joined: 17 Dec 2012
Posts: 636
Location: India
Re: In a certain bathtub, both the hot and cold water fixtures  [#permalink]

Show Tags

New post 05 Jun 2017, 19:03
gautamsubrahmanyam wrote:
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

1.Take an example. C= 1 hr, h= 2 hrs, t=1/(1/1+1/2)=2/3
2.Take a totally different example c=1 hr, h=100hrs, t=1/(1/1+1/100)=100/101
In both the cases I and III are true.
_________________

Srinivasan Vaidyaraman
Sravna Holistic Solutions
http://www.sravnatestprep.com

Holistic and Systematic Approach

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 8174
Premium Member
Re: In a certain bathtub, both the hot and cold water fixtures  [#permalink]

Show Tags

New post 22 Aug 2018, 03:34
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

GMAT Club Bot
Re: In a certain bathtub, both the hot and cold water fixtures &nbs [#permalink] 22 Aug 2018, 03:34
Display posts from previous: Sort by

In a certain bathtub, both the hot and cold water fixtures

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  

Events & Promotions

PREV
NEXT


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.