The IIM Interview Question - Clock
"How many times do the hour and minute hands of a clock overlap in a 24-hour day?"
You may have immediately thought 24 — once per hour.
However, that is not necessarily correct. This question actually tests your deductive reasoning ability and not whether you are able to guess an answer.
Detailed Step By Step Solution
Here is the detailed solution of the question asked in the IIM Interview:
Step 1: What's overlapping?
The hands overlapping means that the hour and minute hands have to be right on top of each other.
Step 2: How many times will the hands overlap in 12 hours?
Most people believe it is 12 times (or once every hour). This is false. Here is why.
The hands do not overlap at 1:00, 2:00, etc.
The hands just barely overlap after every hour. (First hour would be about 1:05ish, second hour about 2:10ish, etc.)
The hands overlap 11 times in 12 hours.
Let's list the times the hands overlap:
12:00
About 1:05
About 2:10
About 3:15
About 4:20
About 5:25
About 6:30
About 7:35
About 8:40
About 9:45
About 10:50
(They don't overlap at 11:55. They just meet again at 12:00.)
Step 3: Now multiply to find the 24 hour clock
A day has two sets of 12 (hour clock):
11 overlaps in 12 hours x 2 = 22 overlaps in 24 hours.
Final Answer is -
The final answer for the question is
The hands of a clock overlap 22 times in a 24-hour day.