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Bunuel
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A particular clock-like device has a round face with three hands. The 18 Jan 2024, 13:45
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E
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55% (hard)

Question Stats:

63% (02:03) correct 37% (02:05) wrong based on 112 sessions

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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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A particular clock-like device has a round face with three hands. The 19 Jan 2024, 01:11
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Bunuel
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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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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A particular clock-like device has a round face with three hands. The 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 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 03 Oct 2024, 00:28
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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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It is possible. But, in this problem I think both are same.

Another example where they meet in place other than starting point like you mentioned.
https://gmatclub.com/forum/three-bodies ... 31449.html

For this partcular question, you can assume clock circumference 60 units. take speed of each as 60units/h , 30u/h and 20u/h. They are at same point which we can also think as 60 units apart.
Relative speed between A and B = 30 u/h => when they cover the distance between them they meet again => t =60/30 = 2 h
" between B and C = 10 u/h => time = 60/10 = 6h
" between A and C = 40 u/h => time = 60/40 = 3/2

lcm of all 3 meeting time = lcm(numerators) / hcf(denominators) = 6/1 hours = 360 minutes
or u can convert h into minute and find lcm.

If I made any mistakes, feel free to correct me

PS: Since, time is directly given you dont need all these steps.
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