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Lucky 7: Mode, Median and Mean!

GMAT-Y4TXUT

You are given a data set {$5$,$7$,$5$,$7$,$5$,$x$,$y$,$z$} whose mode, median, and mean are all $7$.

What is the largest possible value of $z$?

A

$7$

B

$10$

C

$11$

D

$12$

E

$13$