Explanation

In this question, the so-called "decimal with only a finite number of nonzero digits" could be called a terminating decimal, since the number of significant digits terminates at a point. One way that could give a terminating decimal is if it yields an integer. Otherwise, if it yields a fraction such as or , then it terminates (as 0.25 or 0.20, respectively). But if it yields, say , it doesn't terminate. This could get complicated, but we will analyze by cases and remain organized, evaluating the statements separately first.

Statement (1) tells us that q is a factor of 12. It could be 1, 2, 3, 4, 6, or 12. That narrows the field substantially, but we know nothing about p. We can allowably choose p and q to give us or , in two separate cases. Those cases yield different answers to the question, so we do not have sufficient information to answer the question definitively. Statement (1) is insufficient.

Statement (2) allows us to choose the same two cases we were just looking at, so Statement (2) is also insufficient.

Combining the statements, we can still choose the same two cases we were just looking at, and , so the statements combined are insufficient.

The correct answer is (E).