This looks like an inequality problem at first glance, but notice that the inequalities are all > 0. Whenever you see > 0 (positive) or < 0 (negative), think about the question from the point of view of positive and negative values or characteristics.

The question asks whether the sum of *x* and *y* is positive. If you know *x* and *y* are both positive, then the answer to this has to be Yes, but if *x* and *y* are both negative, then the answer has to be No. If one is positive and one is negative, then it depends on which value has the greater magnitude (distance from 0 on a number line).

(1) INSUFFICIENT: Test some cases to see what's possible. You're only allowed to try values for which statement (1) is true.

Case 1: If *x* = 3 and *y* = 2, then *x* – *y* > 0 and so is *x* + *y*. In this case, the answer is Yes, *x* + *y* > 0.

Case 2: If *x* = 2 and *y* = –3, then *x* – *y* > 0 but now *x* + *y* is less than 0, not greater than 0. In this case, the answer is No, *x* + *y* is not greater than 0.

Since it's possible to get both Yes and No answers, this statement is not sufficient to answer the question.

(2) INSUFFICIENT: First, rearrange the inequality given in the statement. *x*^{2} – *y*^{2} is one of the special quadratics and can also be written (*x* + *y*)(*x* – *y*). The statement establishes that (*x* + *y*)(*x* – *y*) > 0. In other words, these two quantities multiply to a positive value. Therefore, it must be the case that either (*x* + *y*) and (*x* – *y*) are both positive or that (*x* + *y*) and (*x* – *y*) are both negative. Since *x* + *y* could be either positive or negative, this statement is not sufficient to answer the question.

(1) AND (2) SUFFICIENT: The second statement establishes that (*x* + *y*) and (*x* – *y*) have to have the same sign—they're either both positive or both negative. The first statement says that (*x* – *y*) is positive. Therefore, (*x* + *y*) must also be positive, so the answer to the question is Always Yes, *x* + *y* > 0.

The correct answer is (C): Both statements together are sufficient to answer the question but neither statement works on its own.