Given distinct positive integers 1, 11,4, x, 2, and 10, which of the following could be the median? Choose the correct answer
A) 3 B) 4 C) 7 D) 8 E) 9
The median of a set with even number of terms is the average of two middle terms when arranged in ascending (or descending) order.   Arrange numbers in ascending order: 1, 2, 4, 9, 11, and x.   Now, x can not possibly be less than 4 as given that all integers are positive and distinct (and we already have 1, 2, and 4).   Next, if x is 4&lt;x&lt;10 then the median will be the average of 4 and x. As all answers for the median are integers, then try odd values for x:   If x=4, then median=(4+4)/2= 
<gadget id="calculator">(4+4)/2</gadget>
<output>4</output>
4 --&gt; OK;   Answer: B.   P.S. If x is more than 9 so 10 or more then the median will be the average of 4 and 9 so  (4+10)/2= 
<gadget id="calculator"> (4+10)/2</gadget>
<output>7</output>
7 (the maximum median possible).
<result>B</result>
Given distinct positive integers 1, 11,4, x, 2, and 10, which of the following could be the median?