Question

Is the positive integer x odd? I) $x^2$ is even II) 4x is even

• A. Statement I alone is sufficient to answer the question
• B. Statement II alone is sufficient to answer the question
• C. Both the statements I and II are sufficient to answer the question but neither statement alone is not sufficient
• D. Both the statements I and II together are not sufficient to answer the question and additional data is required

Hint:

In Data Sufficiency, answering "No" with certainty is just as sufficient as answering "Yes."

Answer 1

The Correct Option is A

Step 1: Concept
If the square of an integer is even, the integer itself must be even. If the square is odd, the integer must be odd.

Step 2: Meaning
We need to determine if $x$ is odd.

Step 3: Analysis
Statement I: $x^2$ is even $\Rightarrow x$ is even. This allows us to answer "No" to the question "Is $x$ odd?". Statement II: $4x$ is always even for any integer $x$ (even or odd), so it doesn't help identify if $x$ is specifically odd.

Step 4: Conclusion
Statement I provides a definitive "No" answer, making it sufficient alone. Final Answer: (A)