Explanation

Before tackling the statement, simplify the complex expression in the question stem:

a^{2} − b^{2} = a^{2} − ab

-b^{2} = -ab

0 = b^{2} − ab

0 = b(b − a)

So either b or (b − a) = 0, but since b ≠ a, (b − a) ≠ 0. b = 0, so we look for a statment that connects c to b.

Statement (1) This statement connects c to a, which we know nothing about. It`s insufficient; the answer must be B, C, or E.

Statement (2) This statement does exactly what we want. c^{3} = 0 = c, so we can answer the question. This statement is sufficient.

**The correct answer is B.**

a

-b

0 = b

0 = b(b − a)

So either b or (b − a) = 0, but since b ≠ a, (b − a) ≠ 0. b = 0, so we look for a statment that connects c to b.

Statement (1) This statement connects c to a, which we know nothing about. It`s insufficient; the answer must be B, C, or E.

Statement (2) This statement does exactly what we want. c