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

If xx is a positive integer, is xx an even number?

(1) xx is a prime number greater than 2.
(2) x+1x + 1 is an odd number.

  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 correct option is the one stating that EACH statement ALONE is sufficient. Statement (1) establishes that xx is an odd prime, yielding a definitive 'No' to the stem question, which makes it sufficient. Statement (2) establishes that xx is even, yielding a definitive 'Yes' to the stem question, making it sufficient as well.

Step-by-Step Solution

1
Analyze Statement (1): xx is a prime number greater than 2.
All prime numbers greater than 2 are odd numbers (e.g., 3, 5, 7, 11). Therefore, xx cannot be an even number. The question 'Is xx an even number?' receives a definitive answer of 'No'. In Data Sufficiency, a statement that leads to a conclusive 'No' is SUFFICIENT.
In Yes/No Data Sufficiency, a consistent 'No' answer is just as sufficient as a consistent 'Yes' answer.
2
Analyze Statement (2): x+1x + 1 is an odd number.
If an integer plus 1 is odd, the integer itself must be even. Thus, xx must be an even number. The question 'Is xx an even number?' receives a definitive answer of 'Yes'. Therefore, Statement (2) is SUFFICIENT.
Direct algebraic or parity properties allow a unique 'Yes' determination.
3
Combine evaluations of both statements.
Since Statement (1) alone yields a definitive 'No' and Statement (2) alone yields a definitive 'Yes', each statement independently answers the question.
Both statements are sufficient on their own.

Key Concept

Definitive Yes/No Sufficiency Rule
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Topics

Value vs. Yes/No Data Sufficiency Decision Logic

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