$36 \cdot 70$ In an examination with $n$ questions, a student answered 15 out of the first 20 questions correctly, and for the remaining questions, he answered $\frac{1}{3}$ correctly. All questions have the same score. If this student's score is $50 \%$, then the number of different values of $n$ is
(A) 4.
(B) 3.
(C) 2.
(D) 1.
(E) This problem cannot be solved.
(10th American High School Mathematics Examination, 1959)
[Solution] Let the score for each question be $t$, then the total score is $n t$. Then the student's score is
$$
15 t+\frac{1}{3} \cdot t(n-20) \text {. }
$$

Given that $\frac{15+\frac{(n-20)}{3}}{n}=50 \%$, solving this yields $n=50$. Therefore, the answer is (D).