2016 AMC 10B Problem 5

Below is the professionally curated solution for Problem 5 of the 2016 AMC 10B, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2016 AMC 10B solutions, or check the answer key.

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Concepts:meanmedian (data)

Difficulty rating: 900

5.

The mean age of Amanda's 44 cousins is 8,8, and their median age is 5.5. What is the sum of the ages of Amanda's youngest and oldest cousins?

 13 \ 13

 16 \ 16

 19 \ 19

 22 \ 22

 25 \ 25

Solution:

The total of the four cousin ages is 48=324\cdot8=32. Since the median is 55, the two middle ages have average 55, so their sum is 1010.

Therefore the youngest and oldest ages sum to 3210=2232-10=22.

Thus, the correct answer is D.

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