Bunuel wrote:
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.
CombinedThe 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