Practice GMAT Data Sufficiency Question

If x and y are integers, what is the sum of x² + 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)	Statement (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

Correct Answer: E

In order for a statement to be sufficient, the data from the statement must ensure that there is one-and-only-one value for the expression x² + y. If there are multiple possible values for this expression, then the statement is not sufficient.
Evaluating Statement (1), we can substitute and write the equation: 4² + y. However, this is not sufficient because if y = 0, x² + y = 4² + 0 = 16 but if y = 1, x² + y = 4² + 1 = 17. Since there are two possible legitimate values for the expression given the information from Statement (1), Statement (1) is NOT SUFFICIENT.
Evaluating Statement (2), we know that y is 4 or -4. We know now that the equation is x² + 4 or x² - 4. However, this statement is not sufficient because if x = 0, the equation could evaluate to 0² + 4 = 4 or 0² - 4 = -4. Since the information from Statement (2) does not allow us to determine one value for the expression, Statement (2) is NOT SUFFICIENT.
When examining Statement (1) and (2) together, we know that the x = 4 and y = 4 or -4. However, these two statements are not sufficient because the expression could evaluate to 4² + 4 = 20 or 4² - 4 = 12. Statements (1) and (2), even when taken together, are NOT SUFFICIENT.