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A particular clock-like device has a round face with three hands. The

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Bunuel
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A particular clock-like device has a round face with three hands. The [#permalink] New post   18 Jan 2024, 13:45
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A particular clock-like device has a round face with three hands. The first hand completes one full rotation every hour, the second hand completes half a rotation per hour, and the third hand completes one-third of a rotation per hour. Initially, all hands are positioned at the 12 o'clock mark and start moving simultaneously. How many minutes will elapse before the hands align together again for the first time since starting?

A. 60
B. 120
C. 180
D. 240
E. 360
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E
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Re: A particular clock-like device has a round face with three hands. The [#permalink] New post   19 Jan 2024, 01:11
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Bunuel wrote:
A particular clock-like device has a round face with three hands. The first hand completes one full rotation every hour, the second hand completes half a rotation per hour, and the third hand completes one-third of a rotation per hour. Initially, all hands are positioned at the 12 o'clock mark and start moving simultaneously. How many minutes will elapse before the hands align together again for the first time since starting?

A. 60
B. 120
C. 180
D. 240
E. 360


Time taken by clock 1 to complete one full rotation = 60 mins

Time taken by clock 2 to complete one full rotation = 120 mins

Time taken by clock 3 to complete one full rotation = 180 mins

Time elapse before the hands align together again for the first time since starting = LCM (60, 120, 180) = 360

Option E
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Re: A particular clock-like device has a round face with three hands. The [#permalink] New post   22 Jan 2024, 00:51
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This solution basically assumes that the only point where they can meet is at the 12 o'clock mark... Isn't it possible they'd meet elsewhere?
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A particular clock-like device has a round face with three hands. The [#permalink] New post   22 Jan 2024, 10:19
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A particular clock-like device has a round face with three hands. The first hand completes one full rotation every hour, the second hand completes half a rotation per hour, and the third hand completes one-third of a rotation per hour. Initially, all hands are positioned at the 12 o'clock mark and start moving simultaneously. How many minutes will elapse before the hands align together again for the first time since starting?

A. 60
B. 120
C. 180
D. 240
E. 360


The three hands of the clock have different rotation speeds:

    • The first hand's period is one rotation in 1 hour.

    • The second hand's period is one rotation in 2 hours.

    • The third hand's period is one rotation in 3 hours.

To find when they align again, we need the least common multiple (LCM) of their rotation periods:

The LCM of 1, 2, and 3 is 6. Therefore, the hands will align again after 6 hours, which is 360 minutes.


Answer: E
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A particular clock-like device has a round face with three hands. The [#permalink]
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