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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

~Education, the Study of Everything


Video Solution

https://youtu.be/8TwlpiWwnJY

~savannahsolver

See Also

2016 AMC 10B (Problems • Answer Key • Resources)
Preceded by
Problem 4 		Followed by
Problem 6
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AMC 10 Problems and Solutions

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