Explanation

This is a number properties question, which means that it will succumb either to analysis by cases, the use of rules, or a combination, such as analysis of cases that leads us to stumble upon a rule. Anyway, the question is straightforward. Let's go to the statements, evaluating them separately first, as always.

We can look at Statement (1) by cases. Given the statement, n could be 31, 41, 51, 131, 1331. In all of those cases, the final digit is 1. Will it be 1 in all cases? Yes, we convince ourselves. Sufficient.

Statement (2) is similar. Let's use cases. The variable n could be 12. It could be 34. Wait: those have different final digits. So Statement (2) does not give sufficient information to determine the final digit of n. Insufficient.

The correct answer is (A).