This is definitely a question where the math is pretty interesting. If you are a math person, the danger here, strategically, is getting sucked into the fun of the math and wasting three minutes. If you are not a math person, the danger here is staring at statement one for three minutes and end up guessing in a panic.
So, this is how I recommend approaching a question like this. First, evaluate the easier statement first. Statement two is NOT sufficient, so eliminate B and D.
Second, set yourself a time budget to evaluate the harder statement. Whatever strategy you choose - math or example numbers being (probably) the two primary strategies - can take a lot of time and you don't want to spend too much time choosing between A, C, and E.
For statement one this is what I would do. First, I would rearrange the equation to look like this:
x(x-6) + y(y-4) = 0
There are two ways that this statement could equal zero.
1. Both parts equal 0 meaning x(x-6)=0 and y(y-4)=0
2. One is positive and the other is negative but with the same absolute value.
Take the easier of the two situations first. If this is the case, x = 6 and y = 4, so |x - y| = |6-4| = 2, which is a factor of 12. So, statement one works at least sometimes.
By this time, you've likely spent at least 2 minutes. Working through 2 (one positive and one negative) is going to take a lot of math or example numbers. DON'T DO THIS. At this point, guess among A, C, and E and move on.
If you are really ahead on time, the arithmetic is probably easier than the math. Make a table and pick some numbers to see what works. I came up with
x y
1 5
6 4 (from above)
This list may not be exhaustive, but for the purposes of the GMAT it is probably fine. For these, |x-y| is a factor of 12. Go with A and move on.
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