Question 1134236
Since the mean is 68, that means the sum of the scores would be 28*68 = 1904.  Let's use the maximum value allowed of 63.  If 23 scores were 63, 23*63 = 1449.  Subtracting that from 1904 leaves 455 "points" to be scored among the remaining 5 students.  This works out to an average of 91 points per student, so yes it is possible.  

Those 23 scores wouldn't be able to be much lower than 63.  The remaining 5 students could get a max of 100 points each, for a total of 500 points.  So that would leave 1904-500=1404 for the 23 students.  1404/23 is about 61 points per student.