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by jamesk486 » Mon Aug 24, 2009 2:23 pm
Working independently at their respective constant rates, pumps X and Y took 48 minutes to fill an empty tank with water. What fraction of the water in the full tank came from pump x?

(1) working alone at its constant rate, pump X would have taken 80 minutes to fill the tank with water.
(1) working alone at its constant rate, pump y would have taken 120 minutes to fill the tank with water.


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Source: — Data Sufficiency |
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by grockit_jake » Mon Aug 24, 2009 3:05 pm
We know that Rx + Ry = Rx+y.

We are given Rx+y = 1/48

(1) gives us Rx = 1/80
(2) gives us Ry = 1/120

Each is sufficient to find the other rate, and once you know each individual rate, you know the proportion of total work done.

As a check, note that 1/80 + 1/120 = 1/48.
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by hpgmat » Tue Aug 25, 2009 12:20 am
grockit_jake wrote:We know that Rx + Ry = Rx+y.

We are given Rx+y = 1/48

(1) gives us Rx = 1/80
(2) gives us Ry = 1/120

Each is sufficient to find the other rate, and once you know each individual rate, you know the proportion of total work done.

As a check, note that 1/80 + 1/120 = 1/48.
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by grockit_jake » Tue Aug 25, 2009 2:08 pm
The goal of the question is to see what is sufficient, not necessarily what the values are.

We don't need to calculate the actual percent that comes from x, but just IF we are able to.
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