, 2019

Combinatorics Difficulty 2.0 Junior Find the answer Netherlands

In a class, $30$ students did a test. Every student got a grade that was an integer from $1$ to $10$ . The grade $8$ was given more often than any of the other grades.
What is the smallest possible average grade of the students?
A) $3\frac{8}{15}$
B) $3\frac{2}{3}$
C) $3\frac{5}{6}$
D) $4\frac{11}{30}$
E) $4\frac{8}{15}$

This was a multiple-choice question, but the options didn't survive into the source we have. The answer given is B, and the solution below works it through.

Solution

B) $3^{\frac{2}{3}}$

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Source: MathNet, licensed CC-BY-4.0. Statement and solution reproduced as published; topic and difficulty added by this site.