3. In a certain chess tournament that only junior high and high school students can participate in, the scoring method is: the winner gets 1 point, the loser gets 0 points, and in a draw, both sides get 0.5 points. Each player plays against every other player once. It is known that the number of high school students is twice that of junior high school students, but their total score is 10 times that of the junior high school students. Then the maximum number of junior high school students participating is ( ).
(A) 2
(B) 3
(C) 4
(D) 5
3. C.

Let the number of junior high school students and senior high school students be $x$ and $2x$ respectively. According to the problem, the total score of all students is 11 times that of the junior high school students, i.e.,
$$
\mathrm{C}_{3 x}^{2} \geqslant 11 \mathrm{C}_{x}^{2} \Rightarrow x \leqslant 4 \text {. }
$$

Therefore, the maximum value of $x$ is 4.
When $x=4$, in the matches between junior high school students and senior high school students, the junior high school students all lose.