First, recognize that x^2 - y^2 = (x + y)(x - y). That makes the expression a little more similar to what we're looking for -- both this and (x + y)^2 contain a (x + y) term.

Statement (1) is insufficient. If y = 3, then x^2 - 9 = 27, so x^2 = 36. x must be either 6 or -6. If x = 6, the answer is (6 + 3)^2 = 81, but if x = -6, the answer is (-6 + 3)^2 = 9.

Statement (2) is sufficient. Since (x + y)(x - y) = 27, if (x - y) = 3, then (x + y) = 9. We're looking for (x + y)^2, which is 9^2 = 81. Choice (B) is correct.