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crazy buses ran over me !

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Re: crazy buses ran over me !

by Stuart@KaplanGMAT » Mon Sep 08, 2008 1:00 am
ashish1354 wrote:this problem takes awfully long if intervals are calculated by counting
cold there be a faster way to solve this?
It really shouldn't take that much scratch work to see that they'll never meet.

Let's just count the hours and ignore the days:

Bus 1: 15:00, 25:00, 35:00, 45:00, 55:00, 65:00...
Bus 2: 16:00, 31:00, 46:00, 61:00, 76:00, 91:00...

Bus 1 is always on the 5:00, Bus 2 is either on the 1:00 or the 6:00 - and never the twain shall meet!
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by Ian Stewart » Mon Sep 08, 2008 4:12 am
If you want to do this algebraically, you want to find the smallest positive integers x and y for which:

3 + 10x = 4 + 15y
10x - 15y = 1
2x - 3y = 1/5

But if x and y are integers, 2x - 3y must be an integer, and could never be equal to 1/5. So it's impossible to find values for x and y.
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