In the set {a,b,c}, the members a,b and c are distinct positive integers such that A is less than B, B is less than C, and C is less than 50, and the mean of the set is an integer value. What is the greatest possible mean?
+248 A
mean=\(\frac{A+B+C}{3}\)
For this to be an intiger, A+B+C must be a multiple of 3.
To get the largest possible mean, the numbers would have to be 47, 48 and 49 are A, B and C, respectivly.
47+48+49 = 144 which is a multiple of 3 so I don't need to try anything else (although the sum of any set of 3 consecutive intigers would be a multiple of 3).
144/3 = \(\boxed{48}\) is the greatest possible mean.
+248 A
mean=\(\frac{A+B+C}{3}\)
For this to be an intiger, A+B+C must be a multiple of 3.
To get the largest possible mean, the numbers would have to be 47, 48 and 49 are A, B and C, respectivly.
47+48+49 = 144 which is a multiple of 3 so I don't need to try anything else (although the sum of any set of 3 consecutive intigers would be a multiple of 3).
144/3 = \(\boxed{48}\) is the greatest possible mean.
