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Word Problem

by Kaunteya1 » Thu Mar 13, 2008 9:32 am
Hey guys, I have a question I need you guys to solve. I don't have the answer, but I am sure someone will figure it out with the answer choices.

Machine A drains a pool. In 4 hours it drains 1/3 of the pool. Once 1/3 of the pool is drained machine B is turned on and together they drain the remaining water in the pool in 6 hours. How many hours would it take machine B by itself to the drain the pool.

A.12
B.16
C.24
D.32
E.48

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by abhi75 » Thu Mar 13, 2008 10:54 am
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.

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by Stuart@KaplanGMAT » Thu Mar 13, 2008 1:19 pm
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?
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by Kaunteya1 » Thu Mar 13, 2008 2:07 pm
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.
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by xilef » Thu Mar 13, 2008 2:31 pm
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. :(
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by netigen » Thu Mar 13, 2008 3:35 pm
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
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by Stuart@KaplanGMAT » Thu Mar 13, 2008 6:51 pm
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.
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