Explanation

Statement (1) There are a limited number of values for x and y that can compose a set E of 5 distinct positive integers of which the largest value is 6: {1, 2, 3, 4, 6}, {1, 2, 4, 5, 6}, and {2, 3, 4, 5, 6}. For each respective possibility, the mean is greater than, less than, and equal to the median. Testing any two sets tell us this statement is insufficient.
The correct answer will be among B/C/E.

Statement (2) Here we have an infinite number of possibilities, and we can test a few extremes to see if we can answer the question stem in different ways. If x and y are very large, the mean of {2, 4, 6, x, y} will be greater than the median of 6. But we can also set x and y such that the mean and median are equal ({2, 3, 4, 5, 6}), or such that the mean is smaller than the median ({2, 4, 6, 7, 8}). This statement alone is insufficient.

The correct answer is C or E. Statement (1 & 2) Given both statements, set E must be {2, 3, 4, 5, 6}, and the mean is equal to the median. Both statements together are sufficient.

**The correct choice is C.**

Statement (2) Here we have an infinite number of possibilities, and we can test a few extremes to see if we can answer the question stem in different ways. If x and y are very large, the mean of {2, 4, 6, x, y} will be greater than the median of 6. But we can also set x and y such that the mean and median are equal ({2, 3, 4, 5, 6}), or such that the mean is smaller than the median ({2, 4, 6, 7, 8}). This statement alone is insufficient.

The correct answer is C or E. Statement (1 & 2) Given both statements, set E must be {2, 3, 4, 5, 6}, and the mean is equal to the median. Both statements together are sufficient.