Question

Is the integer x even?
(1) x + 1 is odd.
(2) x is an integer greater than 1.

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

Hint:

For Data Sufficiency questions about number properties, testing a few small integers is an effective strategy. If you can find one case that gives a "Yes" and another that gives a "No", the statement is not sufficient. If all test cases give the same answer, the statement is likely sufficient.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
This is a Data Sufficiency question that deals with number properties, specifically the properties of even and odd integers. An integer is even if it is divisible by 2, and odd otherwise. Consecutive integers always alternate between even and odd.
Step 2: Detailed Explanation:
Evaluating Statement (1) Alone:
"x + 1 is odd."
If an integer \(k\) is odd, then the integer immediately preceding it, \(k-1\), must be even.
In this case, the integer \(x\) is the one immediately preceding \(x+1\).
Therefore, if \(x+1\) is odd, \(x\) must be even.
This statement provides a definitive "Yes" answer to the question "Is the integer x even?".
So, Statement (1) alone is sufficient.
Evaluating Statement (2) Alone:
"x is an integer greater than 1."
This means \(x\) could be 2, 3, 4, 5, etc.
- If \(x = 2\), the answer is "Yes, x is even."
- If \(x = 3\), the answer is "No, x is not even."
Since we can get both a "Yes" and a "No" answer, this statement does not provide a definitive answer.
So, Statement (2) alone is not sufficient.
Step 3: Final Answer:
Statement (1) alone is sufficient to answer the question, but statement (2) alone is not. This corresponds to option (A).