Explanation

We should always be pleased to see a question that deals with even and odd numbers, because there are rules that apply to arithmetic operations with these numbers, and you don't even really have to remember the rules, because you can easily try numbers to recall them. We want to know whether m-1 is even, or, in other words, whether m is odd. For example, we look at Statement (1) alone. If m+3 is even, then it could be 6, say. In that case, m is 3, which means it's odd. To pick another case, if m+3 is 8, then m is 5--still odd. It will always be odd, because the only way to add an odd number to another, missing, number and obtain an even number as a result is if the missing number is odd. Therefore, we have sufficient information from Statement (1) to answer the question definitively (it doesn't matter whether the answer is Yes or No, so long as it's definitive). So Statement (1) is sufficient. Statement (2) is sufficient by the same logic.

The correct answer is (D).