37. How many times the hour hand and the minute hand coincide in a clock between 10:00 a.m. and 2.00 p.m. (same day)?

1. A. 3 times
2. B. 4 times
3. C. 5 times
4. D. 6 times

Answer: A

Explanation

The hour and minute hands coincide 11 times in every 12-hour period (or 22 times in 24 hours). This is because they coincide once every hour, except for the period between 11 and 1 o’clock, where they coincide only once, exactly at 12 o’clock. Let’s count the coincidences in the given time frame: 10:00 a.m. to 2:00 p.m. (a 4-hour period).
1. Between 10:00 a.m. and 11:00 a.m.: The hands coincide once (around 10:55 a.m.).
2. Between 11:00 a.m. and 12:00 p.m.: The hands coincide exactly at 12:00 p.m. (noon).
3. Between 12:00 p.m. and 1:00 p.m.: The hands coincide only at 12:00 p.m., which has already been counted. There is no other coincidence in this hour.
4. Between 1:00 p.m. and 2:00 p.m.: The hands coincide once (around 1:05 p.m.).
Total coincidences = 1 (10-11) + 1 (at 12:00) + 1 (1-2) = 3 times. This question tests knowledge of clock problems, specifically the relative movement and coincidences of the hands.