Oct 15 12:00 PM PDT  01:00 PM PDT Join this live GMAT class with GMAT Ninja to learn to conquer your fears of long, kooky GMAT questions. Oct 16 08:00 PM PDT  09:00 PM PDT EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth $100 with the 3 Month Pack ($299) Oct 19 07:00 AM PDT  09:00 AM PDT Does GMAT RC seem like an uphill battle? eGMAT is conducting a free webinar to help you learn reading strategies that can enable you to solve 700+ level RC questions with at least 90% accuracy in less than 10 days. Sat., Oct 19th at 7 am PDT Oct 20 07:00 AM PDT  09:00 AM PDT Get personalized insights on how to achieve your Target Quant Score. Oct 22 08:00 PM PDT  09:00 PM PDT On Demand for $79. For a score of 4951 (from current actual score of 40+) AllInOne Standard & 700+ Level Questions (150 questions)
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 23 Jul 2011
Posts: 140
Concentration: Finance, Technology
GPA: 2.99

In a certain bathtub, both the coldwater and the hotwater fixtures
[#permalink]
Show Tags
20 Feb 2012, 15:58
Question Stats:
55% (02:19) correct 45% (02:24) wrong based on 335 sessions
HideShow timer Statistics
In a certain bathtub, both the coldwater and the hotwater fixtures leak. The coldwater leak alone would fill an empty bucket in c hours and the hotwater leak alone would 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 took t hours to fill the bucket, which of the following must be true? I. \(0 < t < h\) II. \(c < t < h\) III. \(\frac{c}{2} < t < \frac{h}{2}\) (A) I only (B) II only (C) III only (D) I and II (E) I and III Attachment:
Gprepps2.JPG [ 51.68 KiB  Viewed 249 times ]
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 58336

Re: In a certain bathtub, both the coldwater and the hotwater fixtures
[#permalink]
Show Tags
20 Feb 2012, 16:19
gmatpunjabi wrote: In a certain bathtub, both the coldwater and the hotwater fixtures leak. The coldwater leak alone would fill an empty bucket in c hours and the hotwater leak alone would 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 took 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  Answer
Can someone please provide a comprehensive explanation as to why statement III is also valid? I. 0 < t < h. That is always correct, as the 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; II. c < t < h. That cannot be correct: \(t\), the 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. III. c/2 < t < h/2. To prove that this is always correct we can use pure logic or algebra. Logic: If both fixtures were leaking at identical rate then \(\frac{c}{2}=\frac{h}{2}=t\) but since \(c<h\) then \(\frac{c}{2}<t\) (as the rate of cold water is higher) and \(t<\frac{h}{2}\) (as the rate of hot water is lower). 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 III is also always true. Answer: E. Hope it's clear.
_________________




Director
Joined: 22 Mar 2011
Posts: 590
WE: Science (Education)

Re: In a certain bathtub, both the coldwater and the hotwater fixtures
[#permalink]
Show Tags
22 Oct 2012, 15:43
carcass wrote: In a certain bathtub, both the coldwater and the hotwater fixtures leak. The coldwater leak alone would fill an empty bucket in c hours, and the hotwater leak alone would 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 took t hours to fill the bucket, which of the following must be true?
I. \(0 < t < h\)
II. \(c < t < h\)
III. \(\frac{c}{2}\) \(< t <\) \(\frac{h}{2}\)
(A) I only
(B) II only
(C) III only
(D) I and II
(E) I and III The two rates for the cold water and that of the hot water fixture are 1/c and 1/h, respectively. We can write the following equation: (1/c+1/h)t = 1, or t/c + t/h = 1. I. t > 0 (represents time to fill the bucket), and from the above inequality it follows that t/h < 1, or t < h. TRUE II. If t > c then t/c > 1, which is impossible according to the above equality. FALSE III. Since t/c + t/h = 1 and c < h, t/c > t/h, necessarily t/h < 1/2 < t/c, or c/2 < t < h/2. TRUE Answer E.
_________________
PhD in Applied Mathematics Love GMAT Quant questions and running.




Manager
Joined: 23 Jul 2011
Posts: 140
Concentration: Finance, Technology
GPA: 2.99

Re: In a certain bathtub, both the coldwater and the hotwater fixtures
[#permalink]
Show Tags
23 Feb 2012, 14:09
I am sorry I do not understand your explanation for statement 3. I do not quite sure how got the inequalities in the algebraic approach and cant seem to understand the logic approach either.



Math Expert
Joined: 02 Sep 2009
Posts: 58336

Re: In a certain bathtub, both the coldwater and the hotwater fixtures
[#permalink]
Show Tags
23 Feb 2012, 15:09
gmatpunjabi wrote: I am sorry I do not understand your explanation for statement 3. I do not quite sure how got the inequalities in the algebraic approach and cant seem to understand the logic approach either. Consider this: say the coldwater leak needs 4 hours to fill an empty bucket and the hotwater leak needs 6 hours to fill an empty bucket. Now, if both leaks needed 4 hours (so if hotwater were as fast as coldwater) then working together they would take 4/2=2 hours to fill the bucket, but we don't have two such fast leaks, so total time must be more than 2 hours. Similarly, if both leaks needed 6 hours (so if coldwater were as slow as hotwater) then working together they would take 6/2=3 hours to fill the bucket, but we don't have two such slow leaks, so total time must be less than 3 hours. So, 4/2<t<6/2 > c/2<t<h/2. Hope it's clear.
_________________



VP
Joined: 02 Jul 2012
Posts: 1105
Location: India
Concentration: Strategy
GPA: 3.8
WE: Engineering (Energy and Utilities)

Re: In a certain bathtub, both the coldwater and the hotwater fixtures
[#permalink]
Show Tags
Updated on: 22 Oct 2012, 22:41
EvaJager wrote: carcass wrote: In a certain bathtub, both the coldwater and the hotwater fixtures leak. The coldwater leak alone would fill an empty bucket in c hours, and the hotwater leak alone would 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 took t hours to fill the bucket, which of the following must be true?
I. \(0 < t < h\)
II. \(c < t < h\)
III. \(\frac{c}{2}\) \(< t <\) \(\frac{h}{2}\)
(A) I only
(B) II only
(C) III only
(D) I and II
(E) I and III The two rates for the cold water and that of the hot water fixture are 1/c and 1/h, respectively. We can write the following equation: (1/c+1/h)t = 1, or t/c + t/h = 1. I. t > 0 (represents time to fill the bucket), and from the above inequality it follows that t/h < 1, or t < h. TRUE II. If t > c then t/c > 1, which is impossible according to the above equality. FALSE III. Since t/c + t/h = 1 and c < h, t/c > t/h, necessarily t/h < 1/2 < t/c, or c/2 < t < h/2. TRUE Answer E. My approach was by just plugging in numbers. I put in \(1\) for c and \(2\) for h and \(\frac{2}{3}\) \(\frac{1}{1} + \frac{1}{2} = \frac{3}{2}\) so., \(c = 1, h = 2, t = \frac{2}{3}, \frac{c}{2} = \frac{1}{2}, \frac{h}{2} = \frac{2}{2} = 1\) \(0<t<c<h\) \(&\) \(\frac{c}{2} < t < \frac{h}{2}\) and I got the answer as E. Did I just get lucky or would it work with any two numbers.
_________________
Originally posted by MacFauz on 22 Oct 2012, 22:24.
Last edited by MacFauz on 22 Oct 2012, 22:41, edited 1 time in total.



Director
Joined: 22 Mar 2011
Posts: 590
WE: Science (Education)

Re: In a certain bathtub, both the coldwater and the hotwater fixtures
[#permalink]
Show Tags
22 Oct 2012, 22:37
MacFauz wrote: EvaJager wrote: carcass wrote: In a certain bathtub, both the coldwater and the hotwater fixtures leak. The coldwater leak alone would fill an empty bucket in c hours, and the hotwater leak alone would 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 took t hours to fill the bucket, which of the following must be true?
I. \(0 < t < h\)
II. \(c < t < h\)
III. \(\frac{c}{2}\) \(< t <\) \(\frac{h}{2}\)
(A) I only
(B) II only
(C) III only
(D) I and II
(E) I and III The two rates for the cold water and that of the hot water fixture are 1/c and 1/h, respectively. We can write the following equation: (1/c+1/h)t = 1, or t/c + t/h = 1. I. t > 0 (represents time to fill the bucket), and from the above inequality it follows that t/h < 1, or t < h. TRUE II. If t > c then t/c > 1, which is impossible according to the above equality. FALSE III. Since t/c + t/h = 1 and c < h, t/c > t/h, necessarily t/h < 1/2 < t/c, or c/2 < t < h/2. TRUE Answer E. My approach was by just plugging in numbers. I put in \(1\) for c and \(2\) for h and \(\frac{2}{3}\) and I got the answer as E. Did I just get lucky or would it work with any two numbers. From the above solution, you can see that any triplet such that c < h and t which fulfill the equation (1/c + 1/h)t = 1 will work. The conclusion doesn't depend on the numbers themselves, but on the relationships between them.
_________________
PhD in Applied Mathematics Love GMAT Quant questions and running.



Intern
Joined: 01 Jan 2013
Posts: 49
Location: India

Re: In a certain bathtub, both the coldwater and the hotwater fixtures
[#permalink]
Show Tags
04 Nov 2013, 03:38
gmatpunjabi wrote: In a certain bathtub, both the coldwater and the hotwater fixtures leak. The coldwater leak alone would fill an empty bucket in c hours and the hotwater leak alone would 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 took 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
Can someone please provide a comprehensive explanation as to why statement III is also valid? t = ch/(c + h) Option 1 : 0 < t < h ch/(c + h) < h i.e c< c + h h > 0 ch/(c + h) > 0 i.e ch > 0 ( c and h not ve) i.e both c & h > 0 Satisfies option 1 Option 2 : c < t < h c < ch/(c + h) c + h < h c < 0 ..False (No need to check other inequality) Option 3 : c/2 < t/2 < h/2 c/2 < ch/(c + h) c + h < 2h c < h (true ,as per question) ch/(c + h) < h/2 2c <c + h c<h (true,as per question)..Hence always true Ans 1 & 3



GMAT Tutor
Joined: 24 Jun 2008
Posts: 1811

Re: In a certain bathtub, both the coldwater and the hotwater fixtures
[#permalink]
Show Tags
03 Jul 2015, 05:18
We know that c < h, so the cold tap fills the tub more quickly than the hot tap. If you turn on both taps, you'll fill the tub more quickly than if you only turn on one tap, so t < c < h, and I is true and II is false (I think there's a typo in the original post  if I recall correctly, in the GMATPrep version of this question, the first roman numeral item reads "t < c < h"). If you had two of the fast taps (the cold taps), they'd fill the tub in c/2 hours. If you had two of the slow taps (the hot taps), they'd fill the tub in h/2 hours. We have one fast tap and one slow tap, so the time they take together must be somewhere in between c/2 and h/2, which is what III says, so III must also be true.
_________________
GMAT Tutor in Toronto
If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com



Director
Joined: 17 Dec 2012
Posts: 626
Location: India

Re: In a certain bathtub, both the coldwater and the hotwater 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 Test Prep http://www.sravnatestprep.comHolistic and Systematic Approach



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15250
Location: United States (CA)

Re: In a certain bathtub, both the coldwater and the hotwater fixtures
[#permalink]
Show Tags
11 Jan 2019, 11:57
Hi All, We're told that 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 took T hours to fill the bucket. We're asked which of the following MUST be true. Based on the five answer choices, we know AT LEAST one of the three Roman Numerals is always true  and we can TEST VALUES to define which are always true and which are not always true. To start, this is an example of a Work Formula question, so we can use the Work Formula: (A)(B)/(A+B) = time it takes to complete the task together, where A and B are the individual times needed to complete the task. In the prompt, we're told that C < H, so we can TEST C = 3 hours, H = 6 hours... meaning that the TOTAL time to fill the bucket would be (3)(6)/(3+6) = 18/9 = 2 hours... so T = 2. With those three values, we can check the Roman Numerals... I. 0 < T < H With our values, T = 2 and H = 6... and 0 < 2 < H, so Roman Numeral 1 appears to be true. Logically, we can also deduce that Roman Numeral 1 will ALWAYS be true, since when BOTH fixtures leak, the amount of time needed to fill the bucket would obviously be SMALLER than if just one of the fixtures was leaking. This means that T < H and T < C will ALWAYS be true and all of those variables will be greater than 0. Eliminate Answers B and C. II. C < T < H With our values, C=3, T = 2 and H = 6... but 3 < 2 < H is NOT true, so Roman Numeral 2 is NOT true Eliminate Answer D. III. C/2 < T < H/2 With our values, C=3, T = 2 and H = 6... and 3/2 < 2 < 6/2 IS true, so Roman Numeral 3 appears to be true. Roman Numeral 3 will also ALWAYS be true, but you would have to do a bit more work to prove it. With ANY pair of C and H that fits the given parameters, we'll end up with a T that is less than both. Since C is the faster rate (in this example, 3 hours to fill a bucket is faster than 6 hours to fill a bucket), if we divide C by 2 and H by 2, then those rates DOUBLE (it would then take just 1.5 hours and 3 hours, respectively, to fill the bucket). That clearly gives us one values that is LESS than the current value of T and one that is MORE than the current value of T. Eliminate Answer A. Final Answer: GMAT assassins aren't born, they're made, Rich
_________________
Contact Rich at: Rich.C@empowergmat.comThe Course Used By GMAT Club Moderators To Earn 750+ souvik101990 Score: 760 Q50 V42 ★★★★★ ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8043
Location: United States (CA)

Re: In a certain bathtub, both the coldwater and the hotwater fixtures
[#permalink]
Show Tags
17 Jan 2019, 19:13
gmatpunjabi wrote: In a certain bathtub, both the coldwater and the hotwater fixtures leak. The coldwater leak alone would fill an empty bucket in c hours and the hotwater leak alone would 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 took 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 We can create the equation: 1/c + 1/h = 1/t If we let c = 2 and h = 3, we have: 1/2 + 1/3 = 3/6 + 2/6 = 5/6. So we see that t = 1/(5/6) = 6/5 = 1.2. So we have t < c < h, so statement I is correct and statement II is not. Let’s now analyze statement III. c/2 = 2/2 = 1 h/2 = 3/2 = 1.5 Thus: c/2 < t < h/2 Answer: E
_________________
5star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews If you find one of my posts helpful, please take a moment to click on the "Kudos" button.



Director
Joined: 24 Oct 2016
Posts: 530
GMAT 1: 670 Q46 V36 GMAT 2: 690 Q47 V38

Re: In a certain bathtub, both the coldwater and the hotwater fixtures
[#permalink]
Show Tags
04 Aug 2019, 05:49
gmatpunjabi wrote: In a certain bathtub, both the coldwater and the hotwater fixtures leak. The coldwater leak alone would fill an empty bucket in c hours and the hotwater leak alone would 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 took 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
Can someone please provide a comprehensive explanation as to why statement III is also valid? If 2 c are working, T = c/2 If 2 h are working, T = h/2 Therefore, if both c and h are working, then c/2 < T < h/2 1) Covers the whole range. MBT 2) Doesn't cover c/2 to c. Not MBT 3) Covers the whole range as calculated above. MBT ANSWER: E
_________________
Most Comprehensive Article on How to Score a 700+ on the GMAT (NEW) Verb Tenses SimplifiedIf you found my post useful, KUDOS are much appreciated. Giving Kudos is a great way to thank and motivate contributors, without costing you anything.



NonHuman User
Joined: 09 Sep 2013
Posts: 13167

Re: In a certain bathtub, both the coldwater and the hotwater fixtures
[#permalink]
Show Tags
11 Oct 2019, 05:50
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 coldwater and the hotwater fixtures
[#permalink]
11 Oct 2019, 05:50






