If $x$ and $y$ are integers, then is $x$ even? Statement I : $x^2 y^2$ is even. Statement II : $1 + x^2 + y^2$ is odd.

Question

Accepted Answer

Select this option if the question can be answered using both the statements together, but cannot be answered using either statement alone

Explanation: We need to determine if x is even. Statement I (x²y² is even): At least one of x or y is even, but x could be odd (y even) or even (y odd/even) — insufficient alone. Statement II (1 + x² + y² is odd): x² + y² must be even, so x and y have the same parity (both even or both odd) — insufficient alone. Combining both: At least one is even (Statement I) and both have same parity (Statement II) → both x and y must be even. Therefore, both statements together uniquely determine that x is even, making Option 3 the correct answer.

Detailed Explanation:

Question 1 of 2 Number Types

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