Explanation

This question gives us an unnecessarily awkward equation. But the situation is simple: we have one equation with two variables. We need to know k. We will get it through knowing m, or possibly through fortuitous algebra. On to the statements, separately first.

Statement (1) gives us m, so we can solve for k. Sufficient.

Statement (2) gives us another equation, so it is probably sufficient. Indeed, multiplying both sides by m, we see that it tells us that k is zero. And the value of k is all we want, and we have it--it's zero. Statement (2) is sufficient.

The correct answer is (D).