Suppose there are 2n+1 students in the class. If n+1 of them score 91, and n of them score the high score h, for the average to be 95, we must have ...
91(n+1) +nh = 95(2n+1)
91n +91 +nh = 190n +95
nh = 99n +4
h = 99 +4/n
The high score must be greater than 99. The high score must be 100.
