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Difficulty: MediumValue vs. Yes/No Data Sufficiency Decision Logic

If mm is a real number, is m>0m > 0?

(1) ∣m+4∣=−3m|m + 4| = -3m
(2) m2+3m+2=0m^2 + 3m + 2 = 0

Which of the following correctly describes the sufficiency of the statements to answer the question?

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

Answer

EACH statement ALONE is sufficient.
The choice stating that EACH statement ALONE is sufficient is correct. Statement (1) restricts mm uniquely to m=−1m = -1 due to the absolute value non-negativity constraint, yielding a definitive 'No' to the question m>0m > 0. Statement (2) yields m=−1m = -1 or m=−2m = -2; since both values are negative, Statement (2) also conclusively answers 'No'. Therefore, both statements independently provide sufficient information.

Step-by-Step Solution

1
Analyze the question stem
The target is a Yes/No question asking whether m>0m > 0. A statement is sufficient if it conclusively proves m>0m > 0 (Yes) or conclusively proves m≤0m \le 0 (No).
Understanding Yes/No Data Sufficiency logic is essential: a definitive 'No' is just as sufficient as a definitive 'Yes'.
2
Evaluate Statement (1): ∣m+4∣=−3m|m + 4| = -3m
Since an absolute value cannot be negative, −3m≥0  ⟹  m≤0-3m \ge 0 \implies m \le 0. Solving m+4=−3mm + 4 = -3m gives 4m=−4  ⟹  m=−14m = -4 \implies m = -1. Solving −(m+4)=−3m-(m + 4) = -3m gives 2m=4  ⟹  m=22m = 4 \implies m = 2 (extraneous because m≤0m \le 0). Thus, m=−1m = -1 uniquely.
Testing m=−1m = -1 in the target question gives: Is −1>0-1 > 0? No. Because Statement (1) provides a single unique value that yields a definitive 'No', Statement (1) alone is sufficient.
3
Evaluate Statement (2): m2+3m+2=0m^2 + 3m + 2 = 0
Factoring gives (m+1)(m+2)=0(m + 1)(m + 2) = 0, so m=−1m = -1 or m=−2m = -2.
If m=−1m = -1, is m>0m > 0? No. If m=−2m = -2, is m>0m > 0? No. Because all possible values for mm consistently lead to a definitive 'No', Statement (2) alone is sufficient.
4
Combine evaluations to select the correct choice
Since Statement (1) alone is sufficient and Statement (2) alone is sufficient, the correct response is that each statement alone is sufficient.
Matches standard GMAT Data Sufficiency Option D.

Key Concept

Value vs. Yes/No Data Sufficiency Decision Logic
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Topics

Value vs. Yes/No Data Sufficiency Decision Logic

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