Problem #1301

1301.

The set $\{3,6,9,10\}$ is augmented by a fifth element $n$ , not equal to any of the other four. The median of the resulting set is equal to its mean. What is the sum of all possible values of $n$ ?

$\mathrm{(A)}\ 7\qquad \mathrm{(B)}\ 9\qquad \mathrm{(C)}\ 19\qquad \mathrm{(D)}\ 24\qquad \mathrm{(E)}\ 26$

This problem is copyrighted by the American Mathematics Competitions.

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Instructions for entering answers:

Reduce fractions to lowest terms and enter in the form 7/9.
Numbers involving pi should be written as 7pi or 7pi/3 as appropriate.
Square roots should be written as sqrt(3), 5sqrt(5), sqrt(3)/2, or 7sqrt(2)/3 as appropriate.
Exponents should be entered in the form 10^10.
If the problem is multiple choice, enter the appropriate (capital) letter.
Enter points with parentheses, like so: (4,5)
Complex numbers should be entered in rectangular form unless otherwise specified, like so: 3+4i. If there is no real component, enter only the imaginary component (i.e. 2i, NOT 0+2i).

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