A set of 5 distinct integers has a mean of 12 and a median of 10. If the smallest integer in the set is 4, what is the greatest possible value for the largest integer in the set?

✓ Correct Answer: Option C

The sum of the 5 integers is 5 * 12 = 60. The integers in ascending order are 4, b, 10, d, e. To maximize 'e', minimize 'b' and 'd'. Min 'b' is 5 (distinct from 4). Min 'd' is 11 (distinct from 10, and >10). So, 4 + 5 + 10 + 11 + e = 60, which yields e = 30.