Explanation

We know that y is an integer and we need to know whether it is less than -5. On the GMAT, and whenever you are so fortunate to deal with algebra and/or negative numbers, you are well served to think of "less" as meaning "to the left on the number line." Most of us have internalized the idea that "less" means "smaller," but this can be confusing since, indeed, it's true that . The confusion vanishes when we think in terms of a number line: -6 is to the left of -5 on the number line, so of course it's less than -5. With that notion always in our minds when we deal with inequalities and negative numbers, let's turn to the data statements, separately first, as always.

Statement (1) tells us that the square of y is greater than 25. Case I: . Case II: . Both cases are allowed, because in both cases the square of y is 36, greater than 25. But the different cases lead to different answers to the question, because 6 is greater than -5 and -6 is less than -5. Therefore, we don't have the information we need to answer the question definitively. Statement (1) alone is insufficient.

Statement (2) is a different animal from Statement (1). Since the cube of y is less than a negative number, y must be a negative number. To take one case, , in which case it's less than -5. Another case: , and y cubed is -64, and that's less than -25, so it's allowed by Statement (2). In that case, y is not less than -5. We have generated opposing answers from cases allowed by the data, so we have insufficient data to answer the question.

We must combine the statements. Combining statements often involves synthesis. If we have analyzed by cases, we can see what cases are still allowed, and this process might lead straight to the answer. Or else, we might be able to infer new conclusions by noticing why some cases that were allowed for a statement alone are no longer allowed. In this question, when the statements are combined, Statement (2) demands the number in question be negative, and this eliminated our Case I from Statement (1).Meanwhile, Statement (1) demands that the absolute value of y be greater than 5, so the case of from Statement (2) is now disallowed. When the statements are combined, y must be negative and it must have an absolute value greater than 5, so it must be less than -5. We can definitively answer (in the affirmative).

The correct answer is (C).