Bunuel wrote:

Is the average (arithmetic mean) of positive integers n and p greater than z?

(1) z > 0

(2) The sum of n and p is 14.

Question: is \(\frac{n+p}{2}>z\)?

(1) z > 0. So z can be any positive integer, but there is no info on n or p; insufficient.

(2) The sum of n and p is 14. So \(\frac{n+p}{2}=14/2=7\), but z could be greater than 7 or less than 7; insufficient.

(1)+(2). We know that z is a positive integers and that the average of n and p is 7, but we cannot determine if the average is greater/less than z; insufficient.

(E) is the answer.