The average (arithmetic mean) of the 5 positive integers k, m, r, s, and t is 16, and k < m < r < s < t. If t is 42, what is the greatest possible value of the median of the 5 integers? Choose the correct option:
A) 17	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 16 which means that in effect, all numbers are equal to 16. If the largest number is 42, it is 26 more than 16. We need r to be maximum so k and m should be as small as possible to get the average of 16. Since all the numbers are positive integers, k and m cannot be less than 1 and 2 respectively. 1 is 15 less than 16 and 2 is 14 less than 16 which means k and m combined are 29 less than the average. 42 is already 26 more than 16 and hence we only have 29 - 26= 
<gadget id="calculator">29 - 26</gadget>
<output>3</output>
3 extra to distribute between r and s. Since s must be greater than r, r can be  16+1= 
<gadget id="calculator"> 16+1</gadget>
<output>17</output>
17 and s can be   16+2= 
<gadget id="calculator">  16+2</gadget>
<output>18</output>
18.   So r is 17.   17nswer (17)
<result>A</result>
The average (arithmetic mean) of the 5 positive integers k, m, r, s, and t is 16, and k < m < r < s < t. If t is 42, what is the greatest possible value of the median of the 5 integers?