Hi btan219,
You're not expected to immediately know the answer to every question that is asked, but if you want to earn points on the GMAT, then you should expect to do the necessary work to figure out what the question asks for. In real basic terms, you have to decide how much work YOU are willing to do to get the correct answer.
Here, we're told that X is a positive integer. We're asked if X is even. This is a YES/NO question.
Fact 1: 9X^2 is divisible by 4
If a pattern doesn't immediately "jump out" at you, then do a bit of work and FIND it (if it exists).
Could X = 1?
9(1^2) = 9 is NOT divisible by 4, so X CANNOT be 1
Could X = 2?
9(2^2) = 36 IS divisible by 4, so X COULD be 2.
In this case, the answer to the question is YES
Could X = 3?
9(3^2) = 81 is NOT divisible by 4, so X CANNOT be 3
Could X = 4?
9(4^2) = 144 IS divisible by 4, so X COULD be 4
In this case, the answer to the question is YES.
Notice the pattern? 9(Odd^2) is NOT divisible by 4, so X CANNOT be odd. Since we were told that X is an integer, then X MUST be even.
Fact 1 is SUFFICIENT
Fact 2: 3X + 2 is divisible by 8
Try taking the same approach with this Fact and see what happens.... Could X be 1, 2, 3, 4 etc.?
Remember that every question you face on the GMAT requires some note-taking and some work. Be prepared to figure things out and 'play around' with prompts as needed and you'll earn the points that you're looking for.
GMAT assassins aren't born, they're made,
Rich