A set of 5 distinct positive integers has a mean of 12 and a median of 13. What is the largest possible integer in the set?

✓ Correct Answer: Option C

The sum of 5 integers with a mean of 12 is 5*12 = 60. Let the distinct positive integers be a < b < 13 < d < e. To maximize e, we minimize a, b, and d. Smallest distinct positive a=1, b=2. So 1+2+13+d+e = 60 => 16+d+e=60 => d+e=44. To maximize e, d must be minimized. Smallest d > 13 is 14. Then e=30. Since 30 isn't an option, for e=29, d=15. The set {1,2,13,15,29} is valid.