Explanation

The functions defined in this question are confusing for a couple of reasons: first, m is a variable and only by coincidence, you could say, does it share the letter with the functions and . The other confusing thing is that, counterintuitively, designates the larger number of a pair and the smaller, not the other way around. With these points in mind, let's turn to the data statements, separately first.

Statement (1) tells us that the larger of the two numbers 100 and n is m. But we don't know what n is. The most streamlined interpretation of this statement is that, by Statement (1), m is at least 100, and therefore what the question is asking for, the minimum of 100 and m, will always be 100. We can illustrate this fact through cases. A possibility, call it Case I, is that . In that case, m would have to be 100, by Statement (1). If m is 100, then is the minimum of 100 and 100, which is 100, and our answer to the question is 100. Case II: . In that case, the maximum value of 100 and m would be n, whatever it is. Therefore, is the minimum of 100 and n, which in this case is greater than 100. Therefore, is 100, and the answer to the question is 100. There is one remaining possible case, which is that , and in that case the answer is also 100. Therefore, we have sufficient information to answer the question. Statement (1) is sufficient.

Statement (2) tells us that m is now the maximum of m and 100. That means, again, that m is equal to or greater than 100. If m is equal to 100, then is the minimum of 100 and 100--and is therefore 100. If m is greater than 100, then is the minimum of 100 and a number greater than 100 and is therefore 100. Either way, is 100. Therefore, we have sufficient information to answer the question. Statement (2) is sufficient.

The correct answer is (D).