A set of five distinct positive integers has a mean of 12. What is the largest possible value for one of these integers?

✓ Correct Answer: Option D

The sum of the five integers is 5 * 12 = 60. To maximize one integer, the other four must be minimized. Statement (1) sets the median, but the other three values can vary. Statement (2) sets the smallest, but other values still vary. Even together, we can't uniquely determine the largest value as other integers can still be adjusted.