Difference between revisions of "2021 JMPSC Accuracy Problems/Problem 2"
Mathdreams (talk | contribs) (→Solution) |
Mathdreams (talk | contribs) (→Solution 2 (Quick and a good way to check your answer)) |
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~Bradygho | ~Bradygho | ||
| − | == Solution 2 | + | == Solution 2 == |
| − | Notice that the average of <math>3</math> numbers that form an arithmetic progression is the median of the numbers. Also, notice that to maximize the average of three numbers, we need to maximize the numbers themselves. Using these observations, it is obvious the answer is <math>\boxed{98}</math> | + | Notice that the average of <math>3</math> numbers that form an arithmetic progression is the median of the numbers. Also, notice that to maximize the average of three numbers, we need to maximize the numbers themselves. Using these observations, it is obvious the answer is <math>\boxed{98}</math>. |
Revision as of 10:26, 11 July 2021
Problem
Three distinct even positive integers are chosen between 
and 
inclusive. What is the largest possible average of these three integers?
Solution
The three biggest distinct positive integers that are 
or less are , 
, and 
. Thus, our answer is 
.
~Bradygho
Solution 2
Notice that the average of 
numbers that form an arithmetic progression is the median of the numbers. Also, notice that to maximize the average of three numbers, we need to maximize the numbers themselves. Using these observations, it is obvious the answer is 
.
