10. At 12:00:00, the hour and minute hands of a clock are overlapped. After how many minutes, for the first time, will they be aligned and opposite?
(A) about 30
(B) about 98
(C) about 100
(D) about 33
(E) about 34
(10) The correct answer is $(D)$.

In one hour, the minute hand travels 360 degrees, while the hour hand travels 30 degrees. In one minute, they travel 6 degrees and half a degree, respectively, so the angle between the two hands widens by 11/2 degrees. For the angle to become 180 degrees, it will take 180/(11/2) = 360/11 minutes, which is approximately 32 minutes and 44 seconds.

Problem proposed by Carmelo Di Stefano.