The point totals that Mark scored in five basketball games were $x, 11,13, y, 12$. How many different possible medians are there for his five point totals?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
In a list of five numbers ordered from smallest to largest, the median is equal to the third (middle) number in the list.

Since $x$ and $y$ must be integers, the values of $x$ and $y$ must belong to exactly one of the following three possibilities:

- each of $x$ and $y$ is less than or equal to 11, or
- each of $x$ and $y$ is greater than or equal to 13 , or
- at least one of $x$ or $y$ is equal to 12 .

If each of $x$ and $y$ is less than or equal to 11, then the median number in the list is 11 .

(In this case, the ordered list could be $x, y, 11,12,13$ or $y, x, 11,12,13$.)

If each of $x$ and $y$ is greater than or equal to 13, then the median number in the list is 13 .

(In this case, the ordered list could be $11,12,13, x, y$ or $11,12,13, y, x$.)

If at least one of $x$ or $y$ is equal to 12, then the list includes $11,12,12,13$ and one other number. When the list is ordered, the two 12s will either be the 2nd and 3rd numbers in the list, or the 3rd and 4th numbers in the list depending on whether the unknown number is less than or equal to 12 or greater than or equal to 12.

In either case, the median is 12 .

Thus, there are three different possible medians for Mark's five point totals.