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

If aa and bb are real numbers, is a+b>0a + b > 0?

(1) a<−2a < -2 and b<−3b < -3
(2) ab>0ab > 0

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

  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.Answer
  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. D
    EACH statement ALONE is sufficient.
  5. E
    Statements (1) and (2) TOGETHER are NOT sufficient.

Answer

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
The correct choice states that Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. Statement (1) leads to a+b<−5a + b < -5, which guarantees that a+ba + b cannot be positive. Because it provides a single, conclusive 'No' answer to the question stem, Statement (1) is sufficient on its own. Statement (2) allows aa and bb to both be positive or both be negative, producing both 'Yes' and 'No' outcomes, so it is not sufficient.

Step-by-Step Solution

1
Understand the Data Sufficiency target.
The target question is a Yes/No question asking whether a+b>0a + b > 0. A statement is sufficient if it yields a consistent 'Yes' OR a consistent 'No'.
In Yes/No Data Sufficiency, a definitive 'No' is just as sufficient as a definitive 'Yes'.
2
Evaluate Statement (1) independently.
Statement (1) gives a<−2a < -2 and b<−3b < -3. Adding the two inequalities gives a+b<−5a + b < -5. Since a+ba + b is strictly less than −5-5, a+ba + b can never be greater than 00.
This yields a definitive 'No' to the question 'Is a+b>0a + b > 0?'. Therefore, Statement (1) ALONE is sufficient.
3
Evaluate Statement (2) independently.
Statement (2) gives ab>0ab > 0, meaning aa and bb share the same sign.
- If a=2a = 2 and b=3b = 3, then a+b=5>0a + b = 5 > 0 (Answer: Yes).
- If a=−2a = -2 and b=−3b = -3, then a+b=−5≯0a + b = -5 \ngtr 0 (Answer: No).
Since Statement (2) can yield both 'Yes' and 'No', Statement (2) ALONE is not sufficient.

Key Concept

Definitive Yes/No Data Sufficiency Decision Logic
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Topics

Value vs. Yes/No Data Sufficiency Decision Logic

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