Explanation

In this question, the question stem doesn't give us a lot of information. We know that both n and m are positive. Also, we should note that these two variables may or may not be integers. We want to know whether m is less than 9 and n is greater than 9. We can move to the data statements, evaluating them separately at first.

Statement (1) looks somewhat like what we are attempting to determine. If m and n were equal and had a product of 81 they would be 9, clearly enough. If one is smaller than the other, and they are both positive, one will have to be less than 9 and one greater. Looks sufficient. We can work algebraically as well. means that . Substituting m into yields



and, since n is positive, we can multiply both sides by n without flipping the sign, and we get



which means that , taking the square root and knowing that n is positive. A similar process confirms that . This precisely confirms what we were looking for, so the Statement (1) is sufficient.

Statement (2) gives us what we ended up obtaining from Statement (1) after algebraic manipulation, so it also is independently sufficient.

The correct answer is (D).