A draining pipe can drain a tank in 12 hours, and a filling pipe can fill the same tank in 6 hours. A total of n pipes – which include both types of pipes – can fill the entire tank in 2 hours. Which of the following could be a value of n? I. 6 II. 7 III. 9

Answer Choices

Correct answer marked below

I only

II only

I and II only

I and III only

Correct

I, II, and III

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Comments

VictoriaJul 23

This one took me way longer than it should have. I kept trying to set up one equation but the trick is that you need to figure out how many of each type could give you a net rate of 1/2 tank per hour. Once I saw that, it clicked.

VighneshAug 2

Same here. The wording made me think there was a single answer at first.

PietroAug 2

Yeah the 'could be' is doing a lot of work in this question.

ReshmaSep 20

Let f be filling pipes and d be draining pipes. Net rate is f/6 - d/12 = 1/2, and f + d = n. After substituting I got f = (n+6)/3, so n+6 has to be divisible by 3. That eliminates one of the options quickly.

GauravSep 30

Nice, that divisibility shortcut is clean. I brute forced it and wasted time.

ManuAug 16

Wait, can someone explain why we're allowed to just add the rates like that? I thought draining pipes make the rate negative, so the total is f/6 - d/12. Is that right?

RajuanAug 25

Yes, draining works against filling, so it's subtracted. The net rate has to equal 1/2 because the tank fills in 2 hours.

HarshAug 24

Right, and since f + d = n, you have two equations and can solve for how many fillers you need.

JuliaSep 14

Is this really a 705+ question? Felt more like a standard rate problem with a small twist. Maybe the trap is assuming all pipes fill.

BookSep 17

The trap is definitely forgetting that some pipes drain. Easy to miss under time pressure.

What this question tests

What it tests

Your ability to combine individual work rates, usually by working with the fraction of a job completed per unit of time.

Common trap

Adding the times instead of the rates, or forgetting to take the reciprocal when combining rates.