Question

Is $(x^2-y^2)$ an odd number?
(I) x and y are integers
(II) x+y is an odd number.

• A. Statement (I) alone is sufficient, but statement (II) alone is not sufficient.
• B. Statement (II) alone is sufficient, but statement (I) alone is not sufficient.
• C. Both statements together are sufficient, but neither statement alone is sufficient.
• D. Each statement alone is sufficient.

Answer 1

The correct option is B Statement (II) alone is sufficient, but statement (I) alone is not sufficient.

From I, we cannot say that $(x^2-y^2)$ is odd nor even.

Statement (II) $\Rightarrow x+y$ is odd $\Rightarrow x$ is even and y is odd or vice versa.
$\Rightarrow x-y$ is odd $\Rightarrow (x^2-y^2)$ is odd.