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Three hoses, x, y, and z, each pump water at a constant rate

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Three hoses, x, y, and z, each pump water at a constant rate

by Mo2men » Sat Mar 18, 2017 7:59 am

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Three hoses, x, y, and z, each pump water at a constant rate. How long will it take the hoses to fill up a 30,000-gallon tank?

(1) Hoses x and z each pump water at constant rate of 120 gallons per hour.
(2) Hose y pumps water at half the rate of x.
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Source: — Data Sufficiency |

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by [email protected] » Sat Mar 18, 2017 10:35 am

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Hi Mo2men,

We're told that 3 pumps each pump water at a constant rate. We're asked how long it would take to fill up a 30,000 gallon tank.

If we're meant to assume that the tank starts off 'empty', then this is a relatively straight-forward prompt (we need the rates of the 3 pumps to answer the question).

1) Hoses X and Z each pump water at constant rate of 120 gallons per hour.

This Fact tells us nothing about the rate of Hose Y, so the answer will vary depending on that rate.
Fact 1 is INSUFFICIENT

2) Hose Y pumps water at half the rate of X.

This Fact tells us nothing about any of the rates, so the answer will vary depending on those rates.
Fact 2 is INSUFFICIENT

Combined, we know....
Hose X = 120 gallons/hour
Hose Z = 120 gallons/hour
Hose Y = 60 gallons/hour

We can now calculate how long it would take to pump 30,000 gallons of water. Again, if we're meant to assume that the tank starts off empty, then this information is SUFFICIENT. IF there's some water in the tank though, then the information is INSUFFICIENT (we would need to know the exact volume of water that needs to be pumped).

Final Answer: C

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by Jay@ManhattanReview » Sun Mar 19, 2017 10:45 pm

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Mo2men wrote:Three hoses, x, y, and z, each pump water at a constant rate. How long will it take the hoses to fill up a 30,000-gallon tank?

(1) Hoses x and z each pump water at constant rate of 120 gallons per hour.
(2) Hose y pumps water at half the rate of x.
Hi Mo2men,

At the outset, it seems to be a simple Time and Rate problem. in fact, it is.

Since there are three hoses, assuming that each of them pumps together and fill an empty tank with a capacity of 30,000 gallons, we need the rates of the three hoses.

It is clear that none of the statements by itself is sufficient, so we need to combine them. Once we combine, we get the rates of the three hoses: x, y and z. The rates are 120, 120/2 = 60, and 120 gallons per hour, respectively. Now the time can be calculated and you are sure to get a unique value. There is no need to calculate. Sufficient.

The correct answer: C

Hope this helps!

Relevant book: Manhattan Review GMAT Data Sufficiency Guide

-Jay
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