31 In the circle $x^{2}+y^{2}-5 x=0$ passing through the point $\left(\frac{5}{2}, \frac{3}{2}\right)$, there are $k(\geqslant 3)$ chords whose lengths form an arithmetic sequence. If the common difference $d \in\left(\frac{1}{6}, \frac{1}{3}\right]$, then the set of values for $k$ is
A. $\{1,2,3\}$
B. $\{3,4,5,6\}$
C. $\{7,8,9\}$
D. $\{1991,1992\}$
31 B. It is known that the longest chord passing through $\left(\frac{5}{2}, \frac{3}{2}\right)$ is 5, and the shortest chord length is 4. From $5 \geqslant 4+(k-1) d$, we get $k \leqslant \frac{1}{d}+1<7$, the chord lengths of $4, 4 \frac{1}{5}, 4 \frac{2}{5}, 4 \frac{3}{5}, 4 \frac{4}{5}, 5$ for 6 chords (or the first 3, 4, 5 chords) meet the requirements. Therefore, the set of values for $k$ is $\{3,4,5,6\}$.