Today’s GMAT challenge question comes from our friends at ManhattanGMAT. To help you with your GMAT studying, try to solve the problem on your own, and then read on for the explanation of its solution:
Problem
If x and y are integers and x < y, what is the value of x + y?
(1) xy = 4
(2) |x| = |y|
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: EACH statement ALONE is sufficient.
E: Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.
Solution
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).
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Read the full article: GMAT Tip: What Is X Plus Y