If y is an integer, is 3^y/10000 > 1

You've made a small mistake with the logarithms. (You don't ever need to use logarithms on the GMAT, by the way, and I've never found a problem where they'd be particularly helpful - so it's a sign that you might be making a problem more complicated than it really is!)

However, here's how the simplification should look, if you choose to simplify it that way:

log(3^y) > log(1000)

y*log(3) > 3

y > 3/log(3) (which is approximately 6.3.)

So, y doesn't have to be greater than 1000, it only has to be greater than ~6.3 for the answer to be 'yes'.

Also, be cautious about using language like "Sufficient to conclude whether or not the statement is true or false." You're never trying to figure out whether the statement is true or false. In fact, you should assume that every statement is always true. The only thing in question is what the answer to the question is.

So, for example, the first part of this problem simplifies to:

"Is y > 6.3?

(1) y >=5 "

It's true that y>=5, but we don't know whether it's greater than or less than 6.3. Therefore, that statement is insufficient.