Is p > q? (1) p^2 > q (2) p^3 > q

The question can be translated as "Does p lie to the right of q on a number line"

------------ q ------------ p ------------

Statement 1

(1) p^2 > q

Case 1: Let's assume p and q are both negative, and p lies to the left of q. In this case, \(p^2 > q\), however p is not greater than q.

------------ p ------------ q ------------ 0 ------------

Case 2: Let's assume p and q are both positive, and p lies to the right of q. In this case, \(p^2 > q\), and p is greater than q.

------------ 0 ------------ q ------------ p ------------

The statement is not sufficient, and we can eliminate A and D.

Statement 2

(2) p^3 > q

Case 1: Let's assume p and q are both negative, and p lies to the left of q. In this case, \(p^3 > q\), however p is not greater than q.

------------ -1------------ p ------------ q ----- \(p^3\) ----- 0 ------------

Case 2: Let's assume p and q are both positive, and p lies to the right of q. In this case, \(p^3 > q\), and p is greater than q.

------------ 0 ------------ q ------------ p ------------

The statement is not sufficient, and we can eliminate B.

Combined

The statements combined do not help as, the regions of Statement 2 are still applicable.

As we can still have two cases, the statements combined are not sufficient.

Option E