Data Sufficiency Question (GMAT)

Question

P and Q are positive integers. Is P odd?

Statement #1: (P2)Q is odd

Statement #2: P + Q is even

Choices:

A - Statement 1 ALONE is sufficient to answer the question, but statement 2 alone is NOT sufficient.

B - Statement 2 ALONE is sufficient to answer the question, but statement 1 alone is NOT sufficient

C - BOTH Statement 1 and 2 TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient

D - EACH statement ALONE is sufficient to answer the question

E - STATEMENT 1 and 2 TOGETHER are not sufficient to answer the questions

Answer 1

Statement 2: odd + odd or even + even = even.

2+2 = 4, even.

3+3 = 6, even.

Statement 2 ALONE is not sufficient. P could be even or odd.

Statement 1:

odd^2 * odd = odd: 3^2 * 3 = 27

odd^2 * even = even: 3^2 * 2 = 18

even^2 * even = even: 2^2 * 2 = 8

even^2 * odd = even: 2^2 * 3 = 12

p has to be odd for p^2 * q to be odd.

Statement 1 ALONE is sufficient.

A