Bunuel wrote:

If j is positive number, is k a positive number?

(1) The average (arithmetic mean) of j and k is positive.

(2) j – k is a positive number.

(1) (j+k)/2 > 0 OR j+k > 0

This means sum of j and k is positive and while j is positive, k could still be negative or positive. Eg, we can have j=2, k=-1 Or j=2, k=1. So Insufficient.

(2) j-k > 0 Or j > k

k could still be positive or negative, so cant say. Insufficient.

Even after combining the two statements, its still insufficient. As explained through examples in first statement. Insufficient.

Hence

E answer