2004 AMC 12B Problem 11

Measure each score as its deviation from the mean $76$

The five $100$s are $120$ points above the mean; each other student is at most $16$ below it

Each score of $100$ is $24$ above the mean, so the five contribute $120$ points above $76.$ These must be balanced by points below the mean, and each remaining student is at most $76 - 60 = 16$ below. So at least $\dfrac{120}{16} = 7.5,$ hence $8$ more students are needed, for a total of $13.$ Five $100$s and eight $61$s achieve this.

Thus, the correct answer is D.