We can do the problem algebraically - the question is asking if (w + x + y + z)/4 > y, or in other words if w + x + y + z > 4y.

Using Statement 1, we can replace "w+z" in the question with "x+y", so our question becomes:

Is w + x + y + z > 4y ?
Is x + y + x + y > 4y ?
Is 2x + 2y > 4y ?
Is 2x > 2y ?
Is x > y ?

and we know the answer to that question is 'no' from the inequality in the stem. So Statement 1 is sufficient to give a 'no' answer to the question. Statement 2 is not sufficient, since our values might be 2, 3, 4, 18, and the answer is 'yes', or 2, 9, 11, 18 and the answer is 'no'.

There's also a conceptual way to see why Statement 1 is sufficient alone. Dividing by 2 on both sides, Statement 1 tells us that the average of the set {w, z} is the same as the average of the set {x, y}. If we combine two sets with identical means, our new set will also have that mean. So the average of the set {w, x, y, z} is the same as the average of x and y. But the average of x and y is the midpoint of x and y on the number line, and when x < y, the midpoint of x and y is less than y. So the average of {w, x, y, z} must be less than y, and the answer must be 'no'.