Difference between revisions of "2000 CEMC Gauss (Grade 8) Problems/Problem 14"
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Latest revision as of 12:55, 20 October 2025
Problem
A set of five different positive integers has an average (arithmetic mean) of 
. What is the largest possible number in this set?
Solution
Let 
be the largest number possible. Because the average is and there are 
numbers, the sum of the numbers must be 
.
To maximize , we can make the first four numbers as small as possible. All of the numbers are distinct and positive, so the first four numbers are 
, 
, 
, and 
. This means that we can set up an equation with :
~anabel.disher
| 2000 CEMC Gauss (Grade 8) (Problems • Answer Key • Resources) | ||
| Preceded by Problem 13 |
Followed by Problem 15 | |
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| CEMC Gauss (Grade 8) | ||
