Odd/ Even and Smart Numbers

[gmatwork]

When dealing with even and odd NUMBERS in D/S, should we test negative numbers allso or only zero and positive values?

When the question stem talks about Odd/Even INTEGERS, should we consider both positive and negative values?

Same question for prime numbers?

When we should and when we should not use Smart numbers in D/S questions?

[jnelson0612]

When dealing with even and odd NUMBERS in D/S, should we test negative numbers allso or only zero and positive values?

When the question stem talks about Odd/Even INTEGERS, should we consider both positive and negative values?

Same question for prime numbers?

When we should and when we should not use Smart numbers in D/S questions?

If the question talks about odd/even integers, you *usually* won't have to deal with negatives. Generally 0 and positive integers will suffice. However, since our goal is to prove insufficiency through number testing, I should always consider any possibility that the question allows, namely:
negatives
fractions
zero
one
square roots

Prime numbers are by definition positive, since the smallest prime number is two.

My process when number testing is this:
1) Plug in any number that is allowed and obtain an answer to the question. Let's say the answer is YES.
2) Stop and consider if there is a number that I can use that would give me the answer of NO. That's when I consider the possibilities listed above. Start trying different possibilities from the list (only those that are allowed by the problem, of course) to see if I can create the opposite answer.