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# A group of 3 small pumps and 1 large pump is filling a tank. Each of t

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GMAT 1: 650 Q44 V35
A group of 3 small pumps and 1 large pump is filling a tank. Each of t [#permalink]

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01 Nov 2014, 09:39
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A group of 3 small pumps and 1 large pump is filling a tank. Each of the 3 small pumps works at 2/3 of the rate of the large pump. If all 4 pumps work at the same time, they will fill the tank in what fraction of the time that it would have taken the large pump had it operated alone?

A. 1/6
B. 1/3
C. 2/3
D. 3/4
E. 4/3
[Reveal] Spoiler: OA

Last edited by Bunuel on 02 Nov 2014, 05:52, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Posts: 43830
Re: A group of 3 small pumps and 1 large pump is filling a tank. Each of t [#permalink]

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02 Nov 2014, 05:57
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jgk wrote:
A group of 3 small pumps and 1 large pump is filling a tank. Each of the 3 small pumps works at 2/3 of the rate of the large pump. If all 4 pumps work at the same time, they will fill the tank in what fraction of the time that it would have taken the large pump had it operated alone?

A. 1/6
B. 1/3
C. 2/3
D. 3/4
E. 4/3

Since 1 small pump works at 2/3 of the rate 1 large pump, then 3 small pumps work at the rate of 3*2/3 = 2 large pumps.

Thus, 3 small pumps and 1 large pump together, work at the rate of 2 + 1 = 3 large pumps. Therefore, together they will do the job in 1/3 the time it would take the large pump to do the job alone.

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Re: A group of 3 small pumps and 1 large pump is filling a tank. Each of t [#permalink]

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03 Nov 2014, 23:58
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Let the work done = 1

Let the rate of big pump = x

Time required by big pump $$= \frac{1}{x}$$ ................ (1)

Rate of each small pump $$= \frac{2x}{3}$$

Combined rate of 3 small & 1 big pump $$= 3*\frac{2x}{3} + x = 3x$$

Time required (All 4 pumps combined) $$= \frac{1}{3x}$$ ............. (2)

$$Fraction = \frac{\frac{1}{3x}}{\frac{1}{x}} = \frac{1}{3}$$

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A group of 3 small pumps and 1 large pump is filling a tank. Each of t [#permalink]

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26 Nov 2017, 08:00
jgk wrote:
A group of 3 small pumps and 1 large pump is filling a tank. Each of the 3 small pumps works at 2/3 of the rate of the large pump. If all 4 pumps work at the same time, they will fill the tank in what fraction of the time that it would have taken the large pump had it operated alone?

A. 1/6
B. 1/3
C. 2/3
D. 3/4
E. 4/3

Rates in tanks/hour
Let large pump fill rate = $$\frac{1}{6}$$

Each small pump's rate is $$\frac{2}{3}$$ of larger pump's rate:
$$(\frac{1}{6}*\frac{2}{3})=(\frac{2}{18})=\frac{1}{9}$$

Three small pumps' combined work rate:
$$(3)(\frac{1}{9})=(\frac{3}{9})=\frac{1}{3}$$

All four pumps' combined work rate is
$$(\frac{1}{6} +\frac{1}{3})=(\frac{3}{6})=\frac{1}{2}$$

Times taken

When Work is 1, rate and time are inversely proportional. Flip the rate to get the time.*

Time taken by large pump alone:
Rate is $$\frac{1T}{6hrs}$$. Time = 6 hours

Time taken by all four:
Rate is $$\frac{1T}{2hrs}$$. Time = 2 hours

Fraction?

Time taken together as a fraction of time taken by large pump alone?

$$\frac{2hrs}{6hrs}=\frac{1}{3}$$

*That is, work, W, is 1 tank to be filled. So for large pump alone, e.g., time, t = $$\frac{W}{r}$$. Rate is $$\frac{1}{6}$$. See below; time taken is the work rate, inverted.

$$\frac{1T}{(\frac{1T}{6hrs})}= 1T * \frac{6hrs}{1T} = 6 hrs$$
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A group of 3 small pumps and 1 large pump is filling a tank. Each of t   [#permalink] 26 Nov 2017, 08:00
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