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

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by BTGmoderatorLU » Mon Jun 24, 2019 3:25 pm

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Source: GMAT Prep

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. \(\frac{c}{2} < t < \frac{h}{2}\)

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

The OA is E
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Source: — Problem Solving |

by Scott@TargetTestPrep » Thu Jun 27, 2019 5:24 pm
BTGmoderatorLU wrote:Source: GMAT Prep

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. \(\frac{c}{2} < t < \frac{h}{2}\)

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

The OA is E

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.

Thus, we have t < c < h, so statement I is correct, and statement II is not correct.

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

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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