Question

Is the number x even?
(1) x + 1 is odd.
(2) x is greater than 0.

• A. Statement (1) alone is sufficient.
• B. Statement (2) alone is sufficient.
• C. Both statements together are sufficient.
• D. Each statement alone is not sufficient.

Hint:

In number properties Data Sufficiency questions, remember the rules: Even + 1 = Odd; Odd + 1 = Even. If you know the parity (evenness or oddness) of \(x+1\), you automatically know the parity of \(x\).

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
This is a Data Sufficiency question concerning the properties of integers (even and odd). The question asks for a definitive "Yes" or "No" answer. Consecutive integers alternate between odd and even.
Step 2: Detailed Explanation:
Evaluating Statement (1) Alone:
"x + 1 is odd."
If a number is odd, the integer immediately preceding it must be even. The integer immediately preceding \(x+1\) is \(x\).
For example, if \(x+1 = 5\) (an odd number), then \(x=4\) (an even number). If \(x+1 = -3\) (an odd number), then \(x=-4\) (an even number).
This is always true. Therefore, we can definitively answer "Yes, x is even."
Statement (1) alone is sufficient.
Evaluating Statement (2) Alone:
"x is greater than 0."
This means \(x\) could be any integer like 1, 2, 3, 4, and so on.
- If we choose \(x = 1\), then x is odd. The answer is "No."
- If we choose \(x = 2\), then x is even. The answer is "Yes."
Since we cannot get a single definitive answer, Statement (2) alone is not sufficient.
Step 3: Final Answer:
Since Statement (1) is sufficient and Statement (2) is not, the correct answer is (A).