What is the Value of m? (1) |m| = −36/m (2) 2m + 2|m| = 0 GMAT Data Sufficiency

Question: What is the value of m?

1. |m| = -36/m
2. 2m + 2|m| = 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.

Correct Option: A

Solution and Explanation:

There is only one approach to this problem.

Approach Solution 1:

(1) |m| = -36/m

The left hand side is an absolute value of a number (|m|), so it’s non-negative, thus the right hand side (-36/m) also must be non-negative, which means that m must be negative. Now, if m is negative, then |m| = -m, so we’d have –m = -36/m, which gives m = -6.

Sufficient.

(2) 2m + 2|m| = 0. This transforms to |m| = -m, which implies only that m is negative or 0.

Not sufficient.

“What is the value of m?”- 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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