Explanation

We are told that n is an integer within a specific range. We will confess that our eyes flitted down at the two data statements to get a sense of what's happening here. That's not a major infraction as long as we are careful to evaluate the statements separately first.

Statement (1) can be paraphrased as saying, "n-1 is even," which can be paraphrased as saying, "n is odd." Double-checking that we're fitting the inequality in the question correctly, we get that n could be 109, 111, 113, or 115. Therefore, we don't have a definitive answer to the question. Statement (1) is insufficient.

Statement (2) is similar. It can be paraphrased as saying, "n is divisible by 3." Note that it doesn't mean, "n is odd." (The definition of odd in these terms would be that a number has a remainder of 1 when divided by 2.) We can see which numbers are divisible by 3 by using the sum of digits rule: 111 gives 1+1+1=3, which is divisible by 3, so 111 is divisible by 3.Double-checking that we're fitting the inequality in the question correctly, we get that n could be 108, 111, or 114. Therefore, we don't have a definitive answer to the question. Statement (2) is insufficient.

Combining the statements is like superimposing the possible cases: only the cases allowed by both statements are still allowed. Between the set {109, 111, 113, 115} and the set {108, 111, or 114} there is only one common element: 111. We can answer the question definitively, so we have sufficient information.

The correct answer is (C).