The average (arithmetic mean) of the 5 positive integers k, m, r, s, and t is 10, and k < m < r < s < t. If t is 20, what is the greatest possible value of the median of the 5 integers?  Choose the most appropriate option:
A) 16 B) 18 C) 13 D) 20 E) 22
We need to find the median which is the third value when the numbers are in increasing order. Since k&lt;m&lt;r&lt;s&lt;t, the median would be r.   The average of the positive integers is 10 which means that in effect, all numbers are equal to 10. If the largest number is 20, it is 10 more than 20. We need r to be maximum so k and m should be as small as possible to get the average of 10. Since all the numbers are positive integers, k and m cannot be less than 1 and 2 respectively. 1 is 9 less than 10 and 2 is 8 less than 10 which means k and m combined are 17 less than the average. 20 is already 10 more than 10 and hence we only have 17 - 10= 
<gadget id="calculator">17 - 10</gadget>
<output>7</output>
7 extra to distribute between r and s. Since s must be greater than r, r can be  10+3= 
<gadget id="calculator"> 10+3</gadget>
<output>13</output>
13 and s can be   10+4= 
<gadget id="calculator">  10+4</gadget>
<output>14</output>
14.   So r is 13.   Answer (13)
<result>C</result>
The average (arithmetic mean) of the 5 positive integers k, m, r, s, and t is 10, and k < m < r < s < t. If t is 20, what is the greatest possible value of the median of the 5 integers?