• NEW! FREE Beat The GMAT Quizzes
Hundreds of Questions Highly Detailed Reporting Expert Explanations
• 7 CATs FREE!
If you earn 100 Forum Points

Engage in the Beat The GMAT forums to earn
100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## In a certain bathtub, both the hot and cold water fixtures tagged by: swerve ##### This topic has 4 expert replies and 0 member replies ### Top Member ## In a certain bathtub, both the hot and cold water fixtures ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult 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, 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 The OA is E Source: GMAT Prep ### GMAT/MBA Expert GMAT Instructor Joined 22 Aug 2016 Posted: 1702 messages Followed by: 28 members Upvotes: 470 Top Reply swerve 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 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 The OA is E Source: GMAT Prep Say c = 10 hours and h = 20 hours since it is given that c < h. Thus, we have 1/c + 1/h = 1/t 1/10 + 1/20 = 1/h h = 20/3 = 6.67 hours Let's see the statements: I. 0 < t < h: 0 < 6.67 < 20. This is correct. II. c < t < h: 10 > 6.66 < 20. This is not correct. III. c/2 < t < h/2: 5 < 6.67 < 10. This is correct. The correct answer: E Hope this helps! -Jay _________________ Manhattan Review Locations: Manhattan Review Chennai | GMAT Prep Himayatnagar | GRE Prep Hyderabad | Bangalore GRE Coaching | and many more... Schedule your free consultation with an experienced GMAT Prep Advisor! Click here. ### GMAT/MBA Expert Elite Legendary Member Joined 23 Jun 2013 Posted: 10020 messages Followed by: 494 members Upvotes: 2867 GMAT Score: 800 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: E GMAT assassins aren't born, they're made, Rich _________________ Contact Rich at Rich.C@empowergmat.com ### GMAT/MBA Expert GMAT Instructor Joined 04 Dec 2012 Posted: 1996 messages Followed by: 237 members Upvotes: 1443 We can easily use logic to get the correct answer, without doing any calculations. In WORK rate problems, when two machines / faucets / people, etc, work together, a) they work at the SUM of their respective rates, and b) the time that it takes them to complete the task together is LESS than the time it took either one individually Thus, the time t for both leaks working together must be less than both c and h. This eliminates II. Time must always be positive, so roman numeral I. works. For III, think of it this way: if two machines both completed a given task in x hrs individually, then when they worked together it would take half the time: x/2. So for our purposes here, imagine that 2 cold faucet leaks would take c/2 hrs... but one cold + one hot would take slightly longer, because the hot faucet leak takes longer. Likewise, 2 hot faucet leaks would take h/2 hrs... but one hot + one cold will take less than that. Thus, the time t must be between c/2 and h/2. Number III works. The answer is E. For more on using logic to estimate the time 2 things spend working together, see: https://www.beatthegmat.com/tank-fill-t286783.html#757795 _________________ Ceilidh Erickson Manhattan Prep GMAT & GRE instructor EdM in Mind, Brain, and Education Harvard Graduate School of Education Manhattan Prep instructors all have 99th+ percentile scores and expert teaching experience. Sign up for a FREE TRIAL, and learn why we have the highest ratings in the GMAT industry! Free Manhattan Prep online events - The first class of every online Manhattan Prep course is free. Classes start every week. ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 1808 messages Followed by: 14 members Upvotes: 43 swerve 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 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. Letâ€™s now analyze statement III. c/2 = 2/2 = 1 h/2 = 3/2 = 1.5 Thus: c/2 < t < h/2 Answer: E _________________ Scott Woodbury-Stewart Founder and CEO • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

Available with Beat the GMAT members only code

• 1 Hour Free
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• Free Trial & Practice Exam
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• Award-winning private GMAT tutoring
Register now and save up to \$200

Available with Beat the GMAT members only code

• Get 300+ Practice Questions

Available with Beat the GMAT members only code

• 5-Day Free Trial
5-day free, full-access trial TTP Quant

Available with Beat the GMAT members only code

• 5 Day FREE Trial
Study Smarter, Not Harder

Available with Beat the GMAT members only code

• Free Practice Test & Review
How would you score if you took the GMAT

Available with Beat the GMAT members only code

### Top First Responders*

1 Jay@ManhattanReview 67 first replies
2 fskilnik@GMATH 51 first replies
3 Brent@GMATPrepNow 48 first replies
4 GMATGuruNY 33 first replies
5 Rich.C@EMPOWERgma... 29 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

### Most Active Experts

1 fskilnik@GMATH

GMATH Teacher

106 posts
2 Brent@GMATPrepNow

GMAT Prep Now Teacher

98 posts
3 Max@Math Revolution

Math Revolution

94 posts
4 Jay@ManhattanReview

Manhattan Review

81 posts
5 GMATGuruNY

The Princeton Review Teacher

77 posts
See More Top Beat The GMAT Experts