$36 \cdot 71$ A certain math test consists of ten multiple-choice questions. The scoring method is: 4 points for each correct answer, -1 point for each wrong answer, and 0 points for not answering. Let the maximum number of possible scores for this test be $n$, then $n$ should be
(A) 42.
(B) 45.
(C) 46.
(D) 48.
(E) None of the above answers is correct.
(Beijing Junior High School Mathematics Competition, 1983)
[Solution] According to the scoring method given in the problem, the minimum score is -10 points (all ten questions answered incorrectly), and the maximum score is 40 points (all ten questions answered correctly). There are 51 possible scores from -10 to 40.

However, answering all ten questions correctly yields 40 points, and answering nine questions correctly yields a maximum of 36 points, so the scores of 39, 38, and 37 cannot be obtained;

When nine questions are answered correctly, only 36 points (nine correct, one blank) or 35 points (nine correct, one incorrect) can be obtained. Therefore, the scores of 34 and 33 cannot be obtained;

When eight questions are answered correctly, only 32 points (eight correct, two blanks), 31 points (eight correct, one incorrect, one blank), or 30 points (eight correct, two incorrect) can be obtained, and 29 points cannot be obtained.

It is easy to verify that all scores from -10 to 28 can be obtained. Therefore, the maximum number of possible scores for this test is $51-3-2-1=45$.
Thus, the answer is $(B)$.