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Here's one where it pays to analyze the question stem a little bit before proceeding.
The question asks for the average of 3x and 6y, two things, and so to find the average you divide that sum by 2. (3x+6y) / 2 can simplify to x+2y. Now it becomes clear that statement 1 suffices.
It shouldn't be too difficult to see why Statement 2 is insufficient. To really nail home that it isn't, one could use examples, though that shouldn't reeeeeally be necessary. Suppose x is 4 and y is 2. That satisfies the statement, and then the average in question is 8. However, it could also be the case that, for example, x is 1 and y is 5. In this case, the average in question is 11. Whatever. (And when I say "average", i'm really just plugging into x+2y). Since we get different answers, it's insufficient.