Yesterday, Manhattan GMAT posted a GMAT question on our blog. Today, they have followed up with the answer:
The question cannot be easily rephrased to incorporate the particular information given. However, of course we should take note that both variables are integers and that x is less than y. We are looking for the value of x + y.
Statement (1): SUFFICIENT. First, we should list out all the possible scenarios in which integers x and y fit the equation xy = 4.
There are three possibilities, as we can find by trial and error: 22 = 4, (-2)2 = 4, and 41 = 4. However, of these possibilities, there is only one for which x is less than y, namely (-2)2 = 4. Thus, we can find the value of x + y, which is -2 + 2 = 0.
Statement (2): SUFFICIENT. Knowing that |x| = |y| does not tell us the values of the integers. However, since they have the same absolute value, but x is less than y, it must be the case that y is a positive integer and x is the negative of that integer. For instance, if y is 5, then x is -5. The sum of x and y must therefore be 0, no matter what.
The correct answer is (D).