n similar pumps, working together, fill the water reservoir

Question

n similar pumps, working together, fill the water tank T in two days. The amount of water, the tank T is capable to contain, is sufficient for 500 persons. Once T is full, pumps take break until the tank becomes empty. This cycle is repeated enough times in 1 month, to secure water for 1,500 persons. 
If in the break of first cycle, after turning on the pumps for two days, half of the pumps become defective, how many days it takes after the first cycle so that all people have water?

(1) The duration of which a full reservoir becomes empty is 1 week.
(2) The pumps are turned on only for a specific time which is two days.

rajatchopra1994 · Answer

Dear  Gumowl  ,

Can you please specify the source of this question.

Regards,
Rajat

Gumowl · Answer

Dear Rajat,

Sorry for the late reply. The source is a well known GMAT quant expert and tutor. Maybe a question like this is unlikely to be in the real GMAT but it helps in the preparations. 
Thank you for your consideration.
Regards,
Gumowl.

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Kinshook · Answer

Given: n similar pumps, working together, fill the water tank T in two days. The amount of water, the tank T is capable to contain, is sufficient for 500 persons. Once T is full, pumps take break until the tank becomes empty. This cycle is repeated enough times in 1 month, to secure water for 1,500 persons.

Asked: If in the break of first cycle, after turning on the pumps for two days, half of the pumps become defective, how many days it takes after the first cycle so that all people have water?

The cycle is repeated equal to or more than 3 times in a month. (500*3 = 1500)
In 2 days, n pumps fill the tank T.
Thereafter, n/2 pumps will fill the tank T in 4 days.

(1) The duration of which a full reservoir becomes empty is 1 week.
First cycle takes takes 2+7 = 9 days
Second cycle takes = 4+7 = 11 days
Third cycle takes = 4+7 = 11 days
It will take 11+11 = 22 days after first cycle so that all people have water.
SUFFICIENT

(2) The pumps are turned on only for a specific time which is two days.
It is not mentioned in what time tank T becomes empty
It does not impact overall time since filling and emptying of pumps will still take same total time.
NOT SUFFICIENT

IMO A

Harshjha001 · Answer

IMO C.

We need the duration in which the full reservoir becomes empty and also the time for which we continue to keep the pumps on.
If it was decided that even if half the pumps are not functioning , the pumps will be kept on only for 2 days than only half the tank will get filled and not exactly 250 people might get served . As it's not stated if all 500 people utilize same amount of water.

I might be overthinking though.

Gumowl · Answer

You are right, you should think about that, but even if you keep half the pumps on for 2 days, then the Tank T will be half full and therefore it needs 3.5 days to become empty, so the cycles will be (2+3.5) for each 250 persons. So in this case also you will get to 4 cycles*(2+3.5)=22 days... No matter how long u turn on the pumps, you will always get 22 days to secure water for the 1,000 persons left.

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Harshjha001 · Answer

Gumowl

Yes , but its not mentioned if all 500 people utilize equal amount of water . We are just told that 500 people can use it for 7 days .
What if in 3.5 days only 200 could use and rest 3.5 days the rest 300 use it.

Gumowl · Answer

Okay, I get you, I hope the edit I made is sufficient for this ambiguity.

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n similar pumps, working together, fill the water reservoir

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