NIMCET 2015 Reasoning PYQ — How many times do the hour and the minute hands of a clock overla… | Mathem Solvex | Mathem Solvex
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NIMCET 2015 — Reasoning PYQ
NIMCET | Reasoning | 2015
How many times do the hour and the minute hands of a clock overlap in 24 h?
Choose the correct answer:
A.
24
B.
22
(Correct Answer)
C.
26
D.
20
Correct Answer:
22
Explanation
1. The 12-Hour Cycle:
The hands of a clock do not overlap every 60 minutes. Because the hour hand also moves, the minute hand actually takes about 65 minutes and 5 seconds to "catch up" and overlap with the hour hand again.
2. The Calculation:
In a 12-hour period, the hands overlap exactly 11 times.
The reason it is 11 and not 12 is because the overlap that would happen between 11:00 and 1:00 occurs exactly at 12:00. Thus, the 11-to-12 and 12-to-1 intervals share a single overlap point.
3. Total in 24 Hours:
Since the day consists of two 12-hour cycles:
11 (overlaps)×2=22 times
Summary of Clock hand movements in 24 hours:
Overlapping (Coincide): 22 times
Straight line (Opposite): 22 times
Right angles (Perpendicular): 44 times
Correct Option: (b) 22
Explanation
1. The 12-Hour Cycle:
The hands of a clock do not overlap every 60 minutes. Because the hour hand also moves, the minute hand actually takes about 65 minutes and 5 seconds to "catch up" and overlap with the hour hand again.
2. The Calculation:
In a 12-hour period, the hands overlap exactly 11 times.
The reason it is 11 and not 12 is because the overlap that would happen between 11:00 and 1:00 occurs exactly at 12:00. Thus, the 11-to-12 and 12-to-1 intervals share a single overlap point.
