The mean (average), the median and the mode of the five numbers $12,9,11,16, x$ are all equal. What is the value of $x$ ?
(A) 9
(B) 11
(C) 12
(D) 13
(E) 16
For the five numbers $12,9,11,16, x$ to have a unique mode, $x$ must equal one of the existing numbers in the list: $12,9,11$, or 16 .

If $x=9$, then the mode is 9 , but the mean of the five numbers $9,9,11,12,16$ is greater than 9 . If $x=16$, then the mode is 16 , but the mean of the five numbers $9,11,12,16,16$ is less than 16 . Therefore, $x$ must either be equal to 11 or 12 .

If $x=11$, the mean of the numbers is $\frac{9+11+11+12+16}{5}=\frac{59}{5}$ which is not equal to the mode 11 . If $x=12$, the mean of the numbers is $\frac{9+11+12+12+16}{5}=\frac{60}{5}=12$ which is equal to the mode 12 . And finally we confirm that if $x=12$, then the median (the middle number in the ordered list $9,11,12,12,16)$ is also equal to 12 .

ANsWER: (C)