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# Buses leave town B at 3 pm and every 10 hours after that.

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Intern
Joined: 26 Jan 2004
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Buses leave town B at 3 pm and every 10 hours after that. [#permalink]

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16 Mar 2004, 12:03
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Buses leave town B at 3 pm and every 10 hours after that. Buses leave town C at 4 pm and every 15 hours after that. If the buses follow this schedule begining on Monday, what is the earliest day on which the buses leave at same time?

A) Monday
B) Tuesday
C) Thursday
D) Sunday
E) So long as they continue operating in this manner,
they will never leave at the same time.

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Director
Joined: 03 Jul 2003
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16 Mar 2004, 12:18
Ans: E

If they start at the same time, they will meet after 30 hours.
Becuase they are starting 1 hour difference, they will never meet.

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Manager
Joined: 27 Feb 2004
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Location: illinois

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16 Mar 2004, 12:19
I just made a few calculations and came to the conclusion that they never meet. Sorry I could not provide a clear cut explaination for this. Usually for these kind of problems, the best method is to find the LCM of the times..but in this case it doesnt seem to work...

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SVP
Joined: 30 Oct 2003
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16 Mar 2004, 12:31

Town Bs schedule is can be expressed as 15+10m (15 is 3 PM )
and Town Cs schedule is 16+15n
16+15n = 15+10m
or m = 1/10 + n + n/2

We have to have m and n as integers
so for m to be integer n/2 = 9/10 because 9/10 + 1/10 = 1 which is an integer.
so n = 9/5 which is not an integer. Hence they will never at the same time.

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Senior Manager
Joined: 02 Mar 2004
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16 Mar 2004, 15:38

3+10m = 4+15n

10m-15n = 1

The above equation has no integer solutions, because (10, 15) does not divide 1.

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16 Mar 2004, 15:38
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