I solved this question using purely trial and error. First I worked out that out of the sequence, 15 + 5 = 20 and 17 + 7 + 9 = 33. This meant x would add onto 20 and 33 to make two different numbers that have the same mean. Then I started trying all the numbers individually from 1-20 in place of x. Finally I came to the answer : 19.
To prove that this answer is correct:
The sequence becomes 15, 5, 19, 7, 9, 17
The mean of the first three numbers ( 15, 5, 19 ) is 15 + 5 + 19 = 39
39 divided by 3 = 13
The mean of the last four numbers ( 19, 7, 9, 17 ) is 19 + 7 + 9 + 17 = 52
52 divided by 4 = 13
Therefore the value of 'x' is 19.