Question

The average of 30 integers is 5. Among these 30 integers, there are exactly 20 which do not exceed 5. What is the highest possible value of the average of these 20 integers?

• A. 4
• B. 3.5
• C. 4.5
• D. 5

Answer 1

Answer: (C)

4.5

Answer 2

Let a be the average of 20 numbers whose average does not exceed 5.
Let b be the average of the remaining 10 numbers. It is evident that $b>5$, meaning the average of these numbers exceeds 5.
Therefore, $30×5=20a+10b$, which simplifies to $2a+b=15.$
This equation leads to $b=15−2a.$
Considering the given options, when $a=4.5, b=6$, satisfying all the given conditions.