Is pq > 0? GMAT Data Sufficiency

Question: Is pq > 0?

2. p < 0

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

Answer: E

Approach Solution (1):
If p = -2, say, then q can be either ½ or -½
And
pq can be positive or negative
Correct option: E

Approach Solution (2):
1).​ is insufficient

2). p < 0 is insufficient
p < 0 is not equal to 0: q = 0.5… p = -2… 2(0.5)^(-2)… pq = -1
p < 0 is not equal to 0: q = -0.5… p = -2... 2(0.5)^(-2) = (-1)² = 1/(-1)² = 1… pq =1
Correct option: E

Approach Solution (3):
Let’s start with easy:
#2. p < 0 but q can be anything < / > / = 0
Insufficient
#1. p can be 0 and at the same time p can be 1
Insufficient
1 + 2
p has to be a –ve value say -1, -2, -1.5 etc
Inside the braces q can be +ve as well as –ve
Put q = ½ and (-1/2) to check
So overall #1 + 2 is also insufficient
Correct option: E

“Is pq > 0?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

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