The average (arithmetic mean) of the 5 positive integers k, m, r, s, and t is 12, 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 correct option:
A) 16	B) 18	C) 19	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 12 which means that in effect, all numbers are equal to 12. If the largest number is 20, it is 8 more than 12. We need r to be maximum so k and m should be as small as possible to get the average of 12. Since all the numbers are positive integers, k and m cannot be less than 1 and 2 respectively. 1 is 11 less than 12 and 2 is 10 less than 12 which means k and m combined are 21 less than the average. 20 is already 8 more than 12 and hence we only have 21 - 8= 
<gadget id="calculator">21 - 8</gadget>
<output>13</output>
13 extra to distribute between r and s. Since s must be greater than r, r can be  12+6= 
<gadget id="calculator"> 12+6</gadget>
<output>18</output>
18 and s can be   12+7= 
<gadget id="calculator">  12+7</gadget>
<output>19</output>
19.   So r is 18.   Answer (20)
<result>D</result>
The average (arithmetic mean) of the 5 positive integers k, m, r, s, and t is 12, and k < m < r < s < t. If t is 20, what is the greatest possible value of the median of the 5 integers?