A set of 10 pipes (set X) can fill 70% of a tank in 7 minutes.

Question

A set of 10 pipes (set X) can fill 70% of a tank in 7 minutes. Another set of 5 pipes (set Y ) fills 3/8 of the tank in 3 minutes. A third set of 8 pipes (set Z) can empty 5/10 of the tank in 10 minutes.

If only half the pipes of set X are closed and only half the pipes of set Y are open and all other pipes are open, how long will it take to fill 49% of the tank?

(a) 16 minutes
(b) 13 minutes
(c) 7 minutes 
(d) 25 minutes
(e) None of these

yashikaaggarwal · Answer

Avinashkr29  I don't think this question is a part of GMAT question bank. 
I will suggest you to stick to official GMAT questions for your exam preparation.

Posted from my mobile device

aviddd · Answer

May I know the source of this question?

IanStewart · Answer

I think the best answer to a question like this is "who cares?" It's not a realistic GMAT question at all, and there isn't anything interesting about math problems that have complications just for the sake of complication. I don't know why anyone would write this, for example: "If only half the pipes of set X are closed and only half the pipes of set Y are open and all other pipes are open". If half of the pipes are open, half are closed, so why does it switch from talking about "half closed" to "half open"? And if there's only one other type of pipe, why does it say "all other pipes" instead of just "pipes of type Z"? Those things make me wonder if the question designer had something in mind different from what they wrote. It also makes no sense to talk about "half the pipes of set Y" when set Y contains 5 pipes. Half of that is 2.5 pipes, which is not an integer. Where is the question from? Anyway:

If 10 pipes fill 70% of a tank in 7 minutes, they fill 100% of the tank in 10 minutes. So 10 pipes of type X fill 1 tank in 10 minutes, and half of those (since that's what the eventual question talks about) will fill 1 tank in 20 minutes.

If 5 pipes fill 3/8 of a tank in 3 minutes, they fill 1 tank in 8 minutes. So 5 pipes of type Y fill 1 tank in 8 minutes, and half of those (which makes no sense, we have 5 pipes) will fill 1 tank in 16 minutes.

If 8 pipes empty 1/2 a tank in 10 minutes, they empty 1 tank in 20 minutes.

So the pipes of type Z are emptying the tank at the same rate as the pipes of type X are filling it. If we only used those pipes, nothing would happen. Only the pipes of type Y then matter. They fill 1 tank in 16 minutes, so 49% of tank in (49/100)(16) minutes, or slightly less than 8 minutes. That's not exactly equal to any answer choice, so E is right.

But since the question writer probably intended something different from what's written, since the question doesn't make sense as written, I won't be surprised if the "OA" is not E.

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A set of 10 pipes (set X) can fill 70% of a tank in 7 minutes.

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