2021 JMPSC Accuracy Problems/Problem 2


Three distinct even positive integers are chosen between $1$ and $100,$ inclusive. What is the largest possible average of these three integers?


The three biggest distinct positive integers that are $100$ or less are $100$, $98$, and $96$. Thus, our answer is $\frac{100+98+96}{3} = \boxed{98}$.


Solution 2

Notice that the average of $3$ 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 $\boxed{98}$.


See also

  1. Other 2021 JMPSC Accuracy Problems
  2. 2021 JMPSC Accuracy Answer Key
  3. All JMPSC Problems and Solutions

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