First, infer everything we can from the given information:

\(w, x\) and \(y\) are positive integers such that \(w \leq x \leq y\)
the average (arithmetic mean) of \(w, x\) and \(y\) is \(20\)
Infer --> the sum of w, x, and y is 60.

Question: is \(w > 15\)?
Since we know that the sum is 60 and w is the smallest value, w would equal 15 if \(x + y = 45\). Thus, w > 15 if \(x + y < 45\).
Rephrased question: is x + y < 45 ?

1) y = 28
This doesn't tell us whether x + y < 45.
But to be sure that it's insufficient, it's best to test cases:

Case 1:
w = 12, x = 20, y = 28
is \(w > 15\)? --> No.

Case 2:
w = 16, x = 16, y = 28
is \(w > 15\)? --> Yes.

Since we can get a "yes" or a "no" answer while keeping the statement true, this is insufficient.

2) One of the three numbers is 17.
Again, this doesn't tell us whether x + y < 45. But to be sure that it's insufficient, we'll test cases again:

Case 1:
w = 17, x = 20, y = 23
is \(w > 15\)? --> Yes.

Case 2:
w = 10, x = 17, y = 33
is \(w > 15\)? --> No.

Since we can get a "yes" or a "no" answer while keeping the statement true, this is insufficient.

(1) & (2) Together: y = 28 and one value = 17.

Since 28 + 17 = 45, then the 3rd value must be 15. And since w is the lowest value, w must equal 15. This is sufficient to answer the question: w is definitively not greater than 15.

The answer is C.