The average of five numbers is $82$. The average of the two smallest numbers is $65$ and the average of the two greatest numbers is $100$. If all five...

Question

The average of five numbers is $82$. The average of the two smallest numbers is $65$ and the average of the two greatest numbers is $100$. If all five numbers are arranged in increasing order, what is the middle number?

Options

A.

$85$

B.

$100$

C.

$70$

D.

$80$

E.

$90$

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