Question

Is $n$ an integer?
(1) $n^2$ is an integer.
(2) $\sqrt{n}$ is an integer.

• A. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
• B. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
• C. Both statements together are sufficient, but neither statement alone is sufficient.
• D. Each statement alone is sufficient.
• E. Statements (1) and (2) together are not sufficient.

Answer 1

The correct option is B Statement (2) alone is sufficient, but statement (1) alone is not sufficient.

$n^2$ is an integer, but $n$ can or cannot be a integer.

So, Statement 1 alone is not sufficient.

If $\sqrt{n}$ is an integer, then $n$ must be an integer.

Statement II alone is sufficient.

Hence. Option B is correct.