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# Working independently at their respective rate, pump X and Y

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Intern
Joined: 16 Apr 2010
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Working independently at their respective rate, pump X and Y [#permalink]

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23 Jul 2010, 14:19
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15% (low)

Question Stats:

100% (00:32) correct 0% (00:00) wrong based on 35 sessions

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1. Working independently at their respective rate, pump 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?

A. Working along at its constant rate, pump X would have taken 80 minutes to fill the tank with water
B. Working alone at its constant rate, pump Y would have taken 120 minutes to fill the tank

Ans-D

2. If K #0, 1 or -1 is 1/k >0

A. 1/k-1 >0
B. 1/k+1>0

Ans-A
[Reveal] Spoiler: OA

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Math Expert
Joined: 02 Sep 2009
Posts: 41893

Kudos [?]: 128870 [1], given: 12183

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23 Jul 2010, 14:44
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Expert's post
1. Working independently at their respective rate, pump 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?

Let the rate of pump X be $$x$$ liters per minute, the rate of pump Y be $$y$$ liters per minute and the capacity of the tank be $$c$$ liters.

Given: $$(x+y)*48=c$$. Question: $$\frac{48x}{c}=?$$ (As from the pump X in 48 minutes would come $$48x$$ liters)

(1) Working along at its constant rate, pump X would have taken 80 minutes to fill the tank with water --> $$80x=c$$ --> $$\frac{48x}{c}=\frac{48x}{80x}=\frac{3}{5}$$. Sufficient.

(2) Working alone at its constant rate, pump Y would have taken 120 minutes to fill the tank --> $$120y=c$$ --> as $$(x+y)*48=c$$, then $$(x+y)*48=120y$$ and $$48x=72y$$ --> $$\frac{48x}{c}=\frac{72y}{120y}=\frac{3}{5}$$. Sufficient.

2. If k#0, 1 or -1 is $$\frac{1}{k}> 0$$?

(1) $$\frac{1}{k-1}> 0$$ --> $$k-1>0$$--> $$k>1$$, hence $$\frac{1}{k}>0$$. Sufficient.

(2) $$\frac{1}{k+1}> 0$$--> $$k+1>0$$ --> $$k>-1$$, hence $$k$$ can be negative as well as positive: $$\frac{1}{k}$$ may or may not be $$>0$$. Not sufficient.

Hope it's clear.

PLEASE POST ONE QUESTION PER TOPIC.
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Re: Working independently at their respective rate, pump X and Y [#permalink]

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14 Feb 2017, 18:40
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Working independently at their respective rate, pump X and Y   [#permalink] 14 Feb 2017, 18:40
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