Is  \(a^7*b^2*c^3>0\) ? (1) bc < 0 (2)ac > 0 GMAT Data Sufficiency

Question: Is \(a^7*b^2*c^3>0\)?

1. bc < 0
2. ac > 0

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are NOT sufficient.

“Is \(a^7*b^2*c^3>0\) ?”– is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken f0rom 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.

Solution and Explanation

Approach Solution 1:

There is only one solution to this problem.

Inequality \(a^7*b^2*c^3>0\) to be true two conditions must be met:

(1)\(a^a\) and \(c^c\) must be either either positive or both negative: in this case \(a^7*c^3\) will be positive;

(2) \(b^b\) must be not being zero: if b = 0, then the entire expression\((a^7*b^2*c^3)\) , irrespective \(a^a\) and \(c^c\) , will be 0, not more than 0.

(1) bc < 0
Hence . Don’t know about a and c.
Therefore, this statement is not sufficient.

(2) ac > 0
Hence, a and c are either both positive or both negative. Don’t know about b: if b = 0, then the expression will be equal to 0.
Therefore, this statement is not sufficient.
(1) + (2) together is sufficient

Correct Answer: C

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