Explanation

We need to know whether n is an integer. We will most likely analyze by cases and by the rules of number properties. On to the data statements, separately first.

Statement (1) tells us that . We can dig into some cases. Say . That's an allowed case, since 18 is an integer. In this case and , so n is not an integer. We can probably find a case that generates a contradictory answer. Say . That's an allowed case, since 27 is an integer. In this case, , so n is an integer. Hence we have contradictory answers from allowed cases, so we have insufficient information to answer the question definitively. Statement (1) is insufficient.

Statement (2) tells us that . That means that





This is similar to Statement (1), but different. Looking at the right side here: any integer times three yields another integer. So we are left with a (different) integer squared, and any integer squared yields another integer. That means that n will always be an integer. We have sufficient information to answer the question definitively, so Statement (2) is sufficient.

The correct answer is (B).