24. A math competition consists of 10 multiple-choice questions. Each correct answer earns 4 points, no answer earns 0 points, and each wrong answer deducts 1 point. If the total score is negative, the grading system will automatically set the total score to zero. How many different total scores are possible?
(A) 35
(B) 36
(C) 37
(D) 41
Answer: A.
Solution: Since negative scores do not appear, the maximum possible scores can be $0,1,2, \cdots 40$, i.e., 41 different total scores. However, when 9 questions are answered correctly, the total scores of $37,38,39,34,33$ cannot appear;

When 8 questions are answered correctly, the total score of 29 cannot appear;
When 7 questions or fewer are answered correctly, all total scores from $0 \sim 28$ are possible,
Therefore, there are $41-5-1=35$ different total scores.