A. Statement (1) ALONE is sufficient, but Statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but Statement (1) alone is not sufficient to answer the question asked.
C. Both Statements (1) and (2) TOGETHER are sufficient to answer the question asked; but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient to answer the question.
Explanation: The question asks: Is \(ab > 0\)? (Is \(ab\) positive?). **Statement 1:** \((a+b)^2 < (a-b)^2\). Expand both sides: \(a^2 + 2ab + b^2 < a^2 - 2ab + b^2\). Subtract \(a^2\) and \(b^2\) from both sides: \(2ab < -2ab\). Add \(2ab\) to both sides: \(4ab < 0\). Divide by 4 (a positive constant): \(ab < 0\). This definitively answers the question as NO, \(ab\) is not positive (it's negative). **Sufficient.**. **Statement 2:** \(a = b\). Case 1: If \(a = b = 1\), then \(ab = 1 \times 1 = 1\). Yes, \(ab\) is positive. Case 2: If \(a = b = 0\), then \(ab = 0 \times 0 = 0\). No, \(ab\) is not positive (it's zero). **Not Sufficient.**. Therefore, Statement (1) ALONE is sufficient, but Statement (2) alone is not sufficient.
