Its a good question. The method didnt occur to me right away but after spending some time so in the exam I would have to make an intelligent guess and move on.
The answer is C. This is how I solved it.

Machine A takes 4 hours for 1/3 and therefore it will take additional 8 hours to do the remaining 2/3 of the work.

We have got the combine time for A and B for 2/3 of the job which is 6 hours.

So by the formula 1/T1 + 1/T2 = 1/6 (total time)

T1 = 8 hours to finish 2/3 of the job
T2 = unknown we have to find.

1/T2 = 1/6 - 1/8 = 2/48 = 1/24

1/T2 = 1/24
Therefore T2 = 24.

Thanks.

For exactly 2 workers, we can write the formula as:

Comb Time (a&b) = a*b/(a+b)

where a and b are their individual times.

In this case, we know that a can clear the entire pool by himself in 12 hours (4 hours * 3).

We also know that a and b can clear the entire pool together in 9 hours (they can clear 2/3 in 6 hours, so 3/3 would take 9 hours).

Plugging in to the formula:

9 = 12*b/(12 + b)

108 + 9b = 12b
108 = 3b
36 = b

Sadly, 36 isn't one of the choices. The thing that I dislike about this question is its ambiguity. When I read "How many hours would it take machine B by itself to the drain the pool?", I immediately interpret that as "the entire pool". However, since 36 isn't the answer, the question must have meant "the remaining 2/3 of the pool". 2/3 of 36 is 24, so that must be the accredited choice.

If this were a real GMAT question (or even a question from a reliable source), it would have been stated much more clearly. Where is this question from?

I don't know where I found this question, I had written it down a while ago. I just knew that it was challanging and I thought I might share it with you guys.

Should we expect questions this ambiguous on GMAT. These questions test your confidence level in your solution. I got 36 an then started looking at my solution to see where I've gone wrong.

Another way to reach the ans

Rate(A) = 1/12 = (1*1/3*1/4)

Rate(B) = x

Total Rate (A+B) = 1/12+x

1/12+x = 2/3 (volume left) div 6 = 2/18 = 1/9

x = 1/36

so 36 for the whole pool and 24 for 2/3 pool

xilef wrote:Should we expect questions this ambiguous on GMAT. These questions test your confidence level in your solution. I got 36 an then started looking at my solution to see where I've gone wrong.

As written, the accredited answer would be 36. There's no way that the currently written question would have an answer of 24 on the real GMAT.