Problem:
Let be a set of nine distinct integers. Six of the elements of the set are , and . What is the number of possible values of the median of
Answer Choices:
A.
B.
C.
D.
E.
Solution:
If nine distinct integers are written in increasing order, the median, which is the middle number, would be in the fifth place. If all of the remaining integers are greater than , then the median is . If all of the remaining integers are less than , then the median is . All the integers from to are possible medians, as shown in the following table.
So, , and are the possible medians, and their count is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions