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Is P > Q ?

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Source: — Data Sufficiency |

by GMATGuruNY » Mon May 29, 2017 10:18 am
I believe that Statement 2 should include the two sets of parentheses shown below:
deepak.kapoor wrote:Is P> Q?
1) P/Q > 1
2) (P-Q)/Q > (P-Q)/P
Statement 1: p/q > 1
Case 1: p=2, q=1
In this case, p>q, so the answer to the question stem is YES.
Case 2: p=-2, q=-1
In this case, p<q, so the answer to the question stem is NO.
INSUFFICIENT.

Case 1 and 2 also satisfy Statement 2.
Since the answer to the question stem is YES in Case 1 but NO in Case 2, the two statements combined are INSUFFICIENT.

The correct answer is E.
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by Jay@ManhattanReview » Mon May 29, 2017 9:12 pm
deepak.kapoor wrote:Is P> Q?

1) P/Q > 1
2) P-Q/Q > P-Q/P
Statement 1: P/Q > 1

If Q is positive, then P > Q. The answer is Yes.

However, if Q is negative, P < Q. For example, say Q = -2 and P = -3, then though P/Q = -3/-2 = 3/2 > 1, P(-3) < Q(-2). The answer is No. Insufficient.

Statement 2: P-Q/Q > P-Q/P

P-Q/Q > P-Q/P

=> P/Q - 1 > 1 - Q/P

=> P/Q + Q/P > 2

=> P^2 + Q^2 > 2PQ

=> P^2 + Q^2 - 2PQ > 0

=> (P - Q)^2 > 0

=> P > Q OR P < Q. Insufficient.

Statement 1 and 2 combined:

The cases discussed in Statement 1 apply in Statement 2 also, thus even combining both the statements would not suffice.

The correct answer: E

Hope this helps!

Relevant book: Manhattan Review GMAT Data Sufficiency Guide

-Jay
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