At what time between 2 and 3 will the hour and minute hands of a clock be 12 minutes divisions apart ?

To find when the hands are 12 minute divisions apart, we convert divisions to degrees. Since one minute division equals 6°, 12 divisions equal 72°. At 2:00, the hour hand is at 60° (30° per hour). Let 'm' be the minutes past 2. The minute hand's position is 6m, and the hour hand's position is 60 + 0.5m. We solve for |(60 + 0.5m) - 6m| = 72. Case 1 (minute hand ahead): 5.5m - 60 = 72, giving 5.5m = 132, so m = 24. Case 2 (hour hand ahead): 60 + 0.5m - 6m = 72, which results in a negative value, meaning it occurred before 2:00. Thus, the hands are 12 divisions apart at exactly 24 minutes past 2 [1]. Options 3 and 4 are identical in the prompt, but 24 minutes is the mathematically correct result.

Sources

1. [1] https://en.wikipedia.org/wiki/Clock_angle_problem