2016 AMC 10B Problem 5

Problem 5 of 25EasierAlgebra

The mean age of Amanda’s

4

cousins is

8,

and their median age is

5.

What is the sum of the ages of Amanda’s youngest and oldest cousins?

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Solution

The total of the four cousin ages is

4\cdot8=32

. Since the median is

5

, the two middle ages have average

5

, so their sum is

10

. Therefore the youngest and oldest ages sum to

32-10=22

. Thus, the correct answer is D.

Concepts: mean · median (data)

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.