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How many times do the hands coincide between the early-morning time on clock A and the late-evening time on clock B, the same day?

Competition practiceClocks
  • A17
  • B18
  • C16
  • D22

Step-by-Step Solution

A shows 5:00 a.m. and B shows 11:00 p.m., 18 hours apart. The hands coincide every 720/11 min, at 12:00, about 1:05, 2:11, … The coincidences after 5:00 a.m. run from about 5:27 a.m. to about 10:55 p.m.: 6 in the morning (5:27 to 10:55), one at noon, and 10 in the afternoon and evening (1:05 to 10:55 p.m.), 17 in all. (18 assumes one per hour; 22 is the count for a full day.)
Answer: A) 17

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