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A clock A rings an alarm first at 9 am, and another clock B also rings
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27 Aug 2024, 02:48
27 Aug 2024, 02:48
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A clock A rings an alarm first at 9 am, and another clock B also rings an alarm first at 9 am. Clock A rings other alarms at intervals of 7 minutes, while clock B rings an alarm at intervals of 8 minutes. Which of the following options represents time at which the two clocks ring alarms simultaneously?
A. 9:14 am
B. 9: 56 am
C. 10:26 am
D. 11:48 am.
A. 9:14 am
B. 9: 56 am
C. 10:26 am
D. 11:48 am.
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Re: A clock A rings an alarm first at 9 am, and another clock B also rings
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29 Aug 2024, 06:45
29 Aug 2024, 06:45
1
The two clocks will ring alarms simultaneously when the time elapsed is a multiple of the LCM of 7 and 8.
Since 7 and 8 do not have any common factors (aside from 1), their LCM is 56.
A. 9:14 am
The time elapsed is 14 minutes.
14 is not a multiple of 56, so this is not a solution.
B. 9:56 am
The time elapsed is 56 minutes.
56 / 56 = 1, so this works.
C. 10:26 am
The time elapsed is 86 minutes.
86 is not a multiple of 56, so this is not a solution.
D. 11:48 am
The time elapsed is 168 minutes.
168 / 56 = 3, so this works.
Since 7 and 8 do not have any common factors (aside from 1), their LCM is 56.
A. 9:14 am
The time elapsed is 14 minutes.
14 is not a multiple of 56, so this is not a solution.
B. 9:56 am
The time elapsed is 56 minutes.
56 / 56 = 1, so this works.
C. 10:26 am
The time elapsed is 86 minutes.
86 is not a multiple of 56, so this is not a solution.
D. 11:48 am
The time elapsed is 168 minutes.
168 / 56 = 3, so this works.
gmatclubot
Re: A clock A rings an alarm first at 9 am, and another clock B also rings [#permalink]
29 Aug 2024, 06:45
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