$29 \cdot 10$ Two or more integers, when divided by $N (N$ is an integer, $N>1)$, if the obtained remainders are the same and non-negative, then mathematically these two or more integers are defined as congruent. If 69, 90, and 125 are congruent for some $N$, then for the same $N$, 81 is congruent to
(A) 3.
(B) 4.
(C) 5.
(D) 7.
(E) 8.
(22nd American High School Mathematics Examination, 1971)
［Solution］The difference between any two congruent integers must be divisible by $N$. Since $90-69=21$ and $125-90=35$, we have $N=7$. Also, since $81 \div 7=11 \cdots \cdots 4$, we know that 81 is congruent to 4. Therefore, the answer is $(B)$.