36.51 Time between 7 and 8 o'clock, when the angle between the hour and minute hands is $84^{\circ}$, the time correct to the nearest minute is
(A) $7: 23$ and $7: 53$.
(B) $7: 20$ and $7: 50$.
(C) 7:22 and $7: 53$.
(D) $7: 23$ and $7: 52$.
(E) $7: 21$ and $7: 49$.
(5th American High School Mathematics Examination, 1954)
[Solution] When the angle between the hour hand and the minute hand is $84^{\circ}$, it is equivalent to the minute hand moving
$$
84^{\circ} \cdot \frac{60}{360^{\circ}}=14 \text { (minutes). }
$$

Let the correct time be 7:$x$ (minutes), noting that when the minute hand moves $x$ minutes, the hour hand moves $\frac{x}{12}$ (minute marks), at this point, the actual position of the hour hand is equivalent to $35+\frac{x}{12}$ (minute marks), so according to the problem, we have
$$
35+\frac{x}{12}=x \pm 14,
$$

which gives $x=\frac{12}{11} \cdot 21 \approx 23$ or $\frac{12}{11} \cdot 49 \approx 53$. Therefore, the answer is $(A)$.