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# Working at a constant rate respectively, pumps X and Y took

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Joined: 21 Jan 2010
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Working at a constant rate respectively, pumps X and Y took [#permalink]

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21 Jan 2010, 17:24
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#33
Working at a constant rate respectively, pumps X and Y took 48 hours to fill an empty water tank. What fraction of the water in a full tank came from pump X?

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

(2) working alone at its constant rate, pump y would have taken 120 minutes to fill up the tank

I am not too sure how this answer is derived. Is it from finding out what fraction of the individual rate is over the rate of X+Y?
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Re: GMAT prep test 2 DS #33 [#permalink]

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21 Jan 2010, 19:47
luminousmocha wrote:
#33
Working at a constant rate respectively, pumps X and Y took 48 hours to fill an empty water tank. What fraction of the water in a full tank came from pump X?

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

(2) working alone at its constant rate, pump y would have taken 120 minutes to fill up the tank

I am not too sure how this answer is derived. Is it from finding out what fraction of the individual rate is over the rate of X+Y?

I hope its 48mins in the question stem

given x and y together take 48mins.
this is derived as 1/X + 1/Y = 1/48 [work-time concept]

stmnt1 - Pump X takes 80mins to fill the tank. here either we can find out the time taken by Y and then doing the calculations to find the ratio.
else since X takes 80mins to fill the tank so in 48mins it will fill 48/80 * 100 = 60% of the tank. hence suff

stmnt2 - we have Y = 120. either we calculate value of X and then find the ratio or similarly since Y takes 120mins
to fill tank then in 48mins it will fill 48/120 * 100 = 40%. the remaining 60% is filled by X. hence suff

so D
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Re: GMAT prep test 2 DS #33 [#permalink]

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17 Feb 2010, 21:46
#33. Ans is D

1/x = ?
given: 1/x + 1/y = 1/48

A. 1/x = 3/4, solving you get y and comparing the two, you get the fraction of tank filled by pump X.
Sufficient

B. 1/y = 1/2, solving you get x and comparing the two, you get the fraction of tank filled by pump X.
Sufficient
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Re: GMAT prep test 2 DS #33 [#permalink]

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25 Jan 2011, 14:20

I'm assuming that both machines take "48 mins" together and not "48 hours"

$$\frac{X*Y}{X+Y} = 48$$

1) X = 80. Sufficient to know the value of Y and, thus, the ratio of work done by each.

2) Y = 120. Sufficient to know the value of X and, thus, the ratio of work done by each.

My vote ... D

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Re: GMAT prep test 2 DS #33 [#permalink]

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25 Jan 2011, 20:18
luminousmocha wrote:
#33
Working at a constant rate respectively, pumps X and Y took 48 hours to fill an empty water tank. What fraction of the water in a full tank came from pump X?

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

(2) working alone at its constant rate, pump y would have taken 120 minutes to fill up the tank

I am not too sure how this answer is derived. Is it from finding out what fraction of the individual rate is over the rate of X+Y?

You can look at it in another way

Stmnt 1: Time taken by X alone : Time taken by X and Y = 80:48 = 5:3
Rate of work of X : Rate of work of X and Y = 3:5 (Work done in both cases is the same. If X alone takes more time, its rate of work is smaller)
So X does 3/5 of total work. Sufficient.
Stmnt 2: Same calculations for y alone with give you that Y does 2/5 of the total work. Sufficient.
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Re: GMAT prep test 2 DS #33   [#permalink] 25 Jan 2011, 20:18
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