Question 108

The average of four consecutive odd numbers is 24. What is the average of the squares of the largest and the smallest of the four numbers?

Solution

The average = 24. So, the numbers are 24 - 3, 24 - 1, 24 + 1 and 24 + 3.
ie. 21, 23, 25, 27
So, the sum of squares = $$21^2 + 27^2 = 441+729 = 1170$$
Hence, the average is $$1170/2 = 585$$

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