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