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Q37·CSAT · Prelims 2024

Evaluating properties of prime and composite numbers

NumericalNumber PropertiesStatement-based● Hard

Question

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)?

Options

a

3 times

Answer
b

4 times

c

5 times

d

6 times

Explanation

Under normal clock dynamics, the minute hand and hour hand coincide exactly once every hour, but with a well-known exception around the 12 o'clock boundary.

Let us trace the intervals from 10:00 a.m. to 2:00 p.m.[cite: 1631, 1632]:

1Between 10:00 a.m. and 11:00 a.m.: Coincide once (at roughly 10:54).
2Between 11:00 a.m. and 1:00 p.m.: The hands do not coincide inside the 11-12 interval or the 12-11 interval independently; they meet exactly at 12:00 sharp. This single meeting covers both hours.
3Between 1:00 p.m. and 2:00 p.m.: Coincide once (at roughly 1:05).

Total meetings = 1 (in 10-11) + 1 (at 12:00) + 1 (in 1-2) = 3 times.

The clock hands coincide exactly 11 times in a 12-hour cycle because the meeting for the 11-12 and 12-1 intervals is consolidated at exactly 12:00.

Answer: (a).

Question details

Year

2024

Paper

CSAT

Question

Q37

Section

Numerical Ability

Sub-topic

Number Properties

Type

Statement-based

Difficulty

Hard

Source hint

Prime numbers properties

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