Explanation

We don't know whether u and v are integers, so they may or may not be, but they are positive. That means that will be less than 1 if and only if u is less than v. If, on the other hand, v is greater than u, then will be greater than 1. For example, and are both less than 1, but and are both greater than 1. We can keep this in mind when evaluating the statements, which we can do separately first.

Statement (1): we already knew that was positive. The fact that it's greater than one when squared means it was already greater than one. That subject is covered in the math review of this course and also in the official testmaker's rubric, and you can see it by playing with numbers. So, we can conclude that . Is that enough to know which is greater? Nope. We can see by cases: u could be a billion and v could be 1, or vice versa. So we don't have sufficient information to identify which is great. Statement (1) is insufficient.

Statement (2), after the first statement, is like a gift. If we had noticed it initially, we might have evaluated it before Statement (1); that's no crime as long as we evaluate each of them separately before even daring to contemplate whether we have to combine them. If we add v to both sides of this statement, we obtain . So we have data that u is larger than v. That means that will always be greater than 1. We have information to answer the question in a manner definitive for all cases, so Statement (2) is sufficient.

The correct answer is (B).