What's mathematically intriguing about this question is that, by definition, the Set in question would have to be infinite. I think I can say, without fear of contradiction, that the GMAT will not ask you about infinite sets. This question is a bit beyond anything you'll see on GMAT math. Nevertheless, I'll show the solution here.
Set I is defined such that, 1). if x is in the set, -x also is in the set. 2). if x and y are in the set, then xy is in the set. Is 12 in the set?
Statement #1: 2 is in the set
Well, if 2 is in the set, then so is -2. Then, their product, -4, must be in the set. Then, the product of -4 with either 2 or -2, and so we go up the powers of 2 and their additive inverses: 8, -8, 16, -16, etc. There is no guarantee that 12 is or isn't in the set, because it's not a power of two. Statement #1, by itself, is insufficient.
Statement #2: -3 is in the set
If -3 is in the set, so is +3. If those two, then -9. Then, powers of three, +27, -27, +81, -81, etc. Again, there is that 12 is or isn't in the set, because it's not a power of three. Statement #2, by itself, is insufficient.
Combined Statements #1 & #2:
Now, if 2 is in the set, as we have seen, so are -2 and -4. If -3 is also in the set, then from the presence of both -3 and -4, we can deduce that (-3)(-4) = 12 is in the set. Thus, combined, the statements are sufficient.
Answer = C
Does that make sense? Please let me know if you have any questions on what I've said.
Mike
