Explanation

This question gives us an unordered list. We don't know whether n and m are greater than the other numbers, or even whether they are integers. Let's evaluate the data statements, separately first.

Statement (1) tells us that m is less than n, but they could be otherwise anything in the wide world of numbers, yielding different values of n and different answers to the question. Therefore, we don't have sufficient information to answer the question, and Statement (1) is insufficient.

Statement (2) gives us more information. Since we are talking about a median of a list, we can start by writing the list in order, first with the elements whose values we know:



We are told the median of the list with n and m added in, wherever they belong, is 109. This limits the possibilities. For example, if n and m were both greater than 121, then the median would be 121, and it's not, so they are not both greater than 121. By this type of logic, we can see that one of the variables must equal 109, and the other one must be something less than 109. But we don't know which is which, so we don't know the value of n. We have insufficient information to answer the question, so Statement (2) is insufficient.

Combining the statements, we can take the work we put into Statement (2) and apply the condition m < n. That condition means that we now know which of the two variables is equal to 109--it must be n. Since , we can definitively answer the question posed. The statements are sufficient together.

The correct answer is (C).