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The Quest for 700: Weekly GMAT Challenge (Answer)

Yesterday, Manhattan GMAT posted a GMAT question on our blog. Today, they have followed up with the answer:

Let t stand for the desired time, so that the drain can empty the tub in t minutes and faucet Q can fill the tub in (t – 4) minutes. Also, the drain does negative work as it empties the tub. The rates for the pipes and the drain are thus

P:

Q:

Drain:

Using the fact that all three fixtures together take 6 minutes to fill 1 tub, set up an RTW chart, and use the chart to calculate the total work quantities (shown in boldface):
Rate (tub/min) Time (min) Work (tubs)
P 1/10 × 6 = 3/5
Q 1/(t – 4) × 6 = 6/(t – 4)
Drain –1/t × 6 = –6/t
Total n/a n/a 1

Set up an equation:

Multiply by the common denominator, 5t(t – 4):

t = 10 OR t = –6

The negative value is absurd, so t = 10; the drain can empty the tub in 10 minutes.
The correct answer is C.



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