2016 AMC 10B Problems/Problem 5

Problem

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?

$\textbf{(A)}\ 13\qquad\textbf{(B)}\ 16\qquad\textbf{(C)}\ 19\qquad\textbf{(D)}\ 22\qquad\textbf{(E)}\ 25$

Solution

The sum of the ages of the cousins is $4$ times the mean, or $32$ . There are an even number of cousins, so there is no single median, so $5$ must be the mean of the two in the middle. Therefore the sum of the ages of the two in the middle is $10$ . Subtracting $10$ from $32$ produces $\textbf{(D)}\ \boxed{22}$ .

Video Solution (CREATIVE THINKING)

https://youtu.be/PHsQWnCkg0Q

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Video Solution

https://youtu.be/8TwlpiWwnJY

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2016 AMC 10B (Problems • Answer Key • Resources)
Preceded by Problem 4	Followed by Problem 6
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All AMC 10 Problems and Solutions

These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions.

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2016 AMC 10B Problems/Problem 5

Contents

Problem

Solution

Video Solution (CREATIVE THINKING)

Video Solution

See Also