Explanation

We should be pleased to see a question about the odd and even properties of numbers, because we know that we can look at cases to summon the number properties rules. We know that m is an integer. Is it odd? On to the data statements, separately first. At a glance, we know they will both be separately sufficient, by the rules. In Statement (1), if is odd, it could be, say, 9. We see that's awkward. How about 37. Then and m is 6, which is even. This will hold up in other cases.

As a tidbit, another way to evaluate this would be to suppose the contrary. You can say, could m be odd? Using the rules, would then be an odd times and odd, so it must be odd. And adding 1 is adding an odd to an odd, so in that case would be even. But that outcome is not permitted by the data statement, which states that must be odd. Ergo m CANNOT be odd, which means that it must be even. That example shows another way of evaluating by cases: you can evaluate by cases whenever you can point to a finite number of possibilities that will cover the universe of possibilities--in this case, that m is odd or m is even.

Statement (2) is sufficient by the same logic.

The correct answer is (D).