AAPL wrote:Manhattan Prep

John and Fawn, each drinking at a constant pace, can finish a case of soda together in 12 hours. How fast can John, drinking alone, finish the case?

1) The average time it would take both to finish independently is 30 hours.
2) It would take John 10 more hours to finish the case drinking alone than it would for Fawn to finish the case.

OA B

Say John alone takes x hours and Fawn takes y hours to finish a can.

Thus, we have 1/x + 1/y = 1/12

We have to get the value of x.

Let's take each statement one by one.

1) The average time it would take both to finish independently is 30 hours.

=> (x + y)/2 = 30 => x + y = 60

From 1/x + 1/y = 1/12, we have (x + y)/xy = 12 => xy = 720. Can't get the unique value of x. Insufficient.

2) It would take John 10 more hours to finish the case drinking alone than it would for Fawn to finish the case.

=> x = 10 + y

From 1/x + 1/y = 1/12, we have From 1/(y + 10) + 1/y = 1/12, we have y = 20. Thus, x = 10 + 20 = 30 hours. Sufficient.

The correct answer is B.

Either this question is not posted correctly or not drafted well. Indeed the correct answer is B, but the information from both the statements are inconsistent. From statement 2, we have the average time it would take both to finish independently = (30 + 20)/2 = 25 hours ≠ 30 hours (given in Statement 1).

A genuine GMAT question would present is a holistic situation in which the question narration, Statement 1 and Statement 2 are consistent with each other or do not contradict. To correct this, Statement 1 should be: The average time it would take both to finish independently is 25 hours.

Hope this helps!

-Jay
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