Bunuel wrote:

A set contains five positive integers, for which the average is 3. What is the greatest possible value of an integer in that set?

A. 5

B. 7

C. 9

D. 11

E. 13

sum of 5 numbers: 5*3=15

now we have to find out greatest possible value. In order to to so we have to minimize all other values of the set. As mentioned all numbers are positive we can set 1 as minimum value for 4 numbers out of 5.

so, 1+1+1+1=4

now we can deduct to find out the max: (sum of of 5 numbers)-(minimum value of 4 numbers)

=15-4

= 11

thus option D is the correct answer.