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Median

For every pos...

Question

For every positive integer $m$ and $n$ such that
$m + 10 < n + 1,$ both the mean and median of the set ${m, m + 4, m + 10, n + 1, n + 2, 2 n}$ are equal to $n .$ The value of $m + n$ is equal to

5

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21

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16

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11

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Solution

The correct option is B $21$
Given, Mean $=$ Median $= n$
$\Rightarrow \frac{3 m + 4 n + 17}{6} = \frac{(m + 10) + (n + 1)}{2} = n$
$\Rightarrow 3 m + 17 = 2 n$ and $m + 11 = n$
Solving the two equations, we get
$m = 5, n = 16$
$∴ m + n = 21$

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