Question: Is pq < 0?

1. 14|p| + |q| = 0
2. |p| + 14|q| = 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: D

Approach Solution (1):
1). 14|p| + |q| = 0
Both |p| and |q| have to be non-negative
So the LHS will be positive or 0 if both p and q are 0
So pq = 0
Hence our answer is No for pq < 0
Sufficient
2). |p| + 14|q| = 0
Both |p| and |q| have to be non-negative
So the LHS will be positive or 0 if both p and q are 0
So pq = 0
Hence our answer is No for pq < 0
Sufficient
Correct option: D

Approach Solution (2):
S1: says both |p| and |q| have to be non-negative
So pq = 0
But if pq < 0, the answer will be No
Hence sufficient
Similarly for S2, it is sufficient
Correct option: D

Approach Solution (3):
S1:
|p| and |q| are non-negative
14|p| + |q| = positive or 0
For pq < 0, the answer will be o
Hence this statement is sufficient
S2:
|p| and |q| are non-negative
|p| + 14|q| = positive or 0
For pq < 0, the answer will be o
Hence this statement is sufficient
Correct option: D

“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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