Meaning there is a number which appears most often.
Thus, there are three possibilities:
1)Mode is 25 ( .
2)Mode is 19 ( .
3)Mode is 39 ( ).
It cannot be case #3 because then the mean is 29.2 a violation of initial conditions of problem.
If #2 then the mean must be 19.
Checking the mode we find that this works.
If #1 then the mean must be 25.
But the problem says it is not amongs the numbers.
Thus, we have determined the unique numbers the work.