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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?

 Jun 13, 2019
edited by Guest  Jun 13, 2019
edited by Guest  Jun 13, 2019
edited by Guest  Jun 13, 2019

Best Answer 

 #1
avatar+99 
+2

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.

 Jun 13, 2019
 #1
avatar+99 
+2
Best Answer

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.

power27 Jun 13, 2019
 #2
avatar
+1

thanks

 Jun 13, 2019

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