Is P> Q?
1) P/Q > 1
2) P-Q/Q > P-Q/P
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Is P > Q ?
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deepak.kapoor
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GMATGuruNY
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I believe that Statement 2 should include the two sets of parentheses shown below:
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.
Statement 1: p/q > 1deepak.kapoor wrote:Is P> Q?
1) P/Q > 1
2) (P-Q)/Q > (P-Q)/P
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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Statement 1: P/Q > 1deepak.kapoor wrote:Is P> Q?
1) P/Q > 1
2) P-Q/Q > P-Q/P
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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