Question

If $a^6-b^6=0$, then what is the value of $a^3-b^3$?
(1) a is positive
(2) b is greater than 1

• A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient
• B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient
• C. BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient
• D. Statements (1) and (2) TOGETHER are NOT sufficient

Answer 1

The correct option is C BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient

a6−b6=0a6−b6=0
⇒(a3b3)(a3−b3)=0⇒(a3b3)(a3−b3)=0
(1) and (2) ⇒a3+3>0⇒a3+3>0
Hence a3−b3=0a3−b3=0
∴∴ Both statements together are necessary to answer the question.