Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 04 Dec 2009
Posts: 19

In a certain bathtub, both the hot and cold water fixtures
[#permalink]
Show Tags
Updated on: 22 Feb 2013, 01:49
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
Official Answer and Stats are available only to registered users. Register/ Login.
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.




Math Expert
Joined: 02 Sep 2009
Posts: 49430

Re: GMAT Prep2  Time and Work Problem.Please help
[#permalink]
Show Tags
04 Feb 2010, 06:16
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? Extrahard Quant Tests with Brilliant Analytics




Intern
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
29 Jan 2010, 03:44
Answer is 5If 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
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
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
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
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 algebrafree 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
Joined: 03 Sep 2006
Posts: 833

Re: GMAT Prep2  Time and Work Problem.Please help
[#permalink]
Show Tags
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
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
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 algebrafree 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
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
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 algebrafree 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
Joined: 13 Aug 2009
Posts: 134
WE 1: 4 years in IT

Gmat prep ps2
[#permalink]
Show Tags
28 Mar 2010, 11:01
Attachments
Gprepps2.JPG [ 52.72 KiB  Viewed 7923 times ]



Manhattan Prep Instructor
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
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 < h0 < 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
Joined: 28 Dec 2010
Posts: 23

Re: Gmat prep ps2
[#permalink]
Show Tags
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
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
02 Sep 2012, 13:17
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
Joined: 13 Aug 2012
Posts: 436
Concentration: Marketing, Finance
GPA: 3.23

Re: In a certain bathtub,both the hot and cold water fixtures
[#permalink]
Show Tags
14 Nov 2012, 06:33
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 TRUEII. 4 < \(\frac{20}{9}\) < 5 FALSEIII. 2 < 20/9 < 5/2 TRUE!Answer: E
_________________
Impossible is nothing to God.



Intern
Joined: 08 Dec 2012
Posts: 7
Location: United States
Concentration: Finance, Strategy
GPA: 3.71
WE: Sales (Energy and Utilities)

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.



Math Expert
Joined: 02 Sep 2009
Posts: 49430

Re: In a certain bathtub,both the hot and cold water fixtures
[#permalink]
Show Tags
22 Feb 2013, 01:51



Director
Joined: 17 Dec 2012
Posts: 636
Location: India

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



NonHuman User
Joined: 09 Sep 2013
Posts: 8174

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




Re: In a certain bathtub, both the hot and cold water fixtures &nbs
[#permalink]
22 Aug 2018, 03:34






