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Q. Every move up or down is 1 unit. Minimum distance between

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Intern
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Q. Every move up or down is 1 unit. Minimum distance between [#permalink] New post 09 Feb 2008, 20:24
Q. Every move up or down is 1 unit. Minimum distance between X and Y is 5 units. How many such paths exist in the diagram?

Image

A. Six
B. Eight
C. Ten
D. Eighteen
E. Twenty

The answer is C. Ten.
My question is - is there a way to calculate this easily without listing out the different paths?
Director
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Re: Number shortest paths from X to Y [#permalink] New post 09 Feb 2008, 20:31
Are you sure that is the officially answer? I would have guessed 6 (always have to go 2 ways over and 3 down, 2*3 = 6). There is a question like this in the OA as well.
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Re: Number shortest paths from X to Y [#permalink] New post 09 Feb 2008, 23:37
5! / 3! 2!

five slots to move. 3 up 2 right. those are the repeats.
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Director
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Re: Number shortest paths from X to Y [#permalink] New post 11 Feb 2008, 04:41
You can solve it combinatorically, or visually. Or both.

I just scan it visually.
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Re: Number shortest paths from X to Y [#permalink] New post 11 Feb 2008, 09:47
Yes the answer is:
5! / 3! 2!

There are 5 slots to fill. There are 3 repetitions of up and 2 repetitions of the formula is the above. The denominator should contain the number of repetitions of the components.

Thanks!
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Re: Number shortest paths from X to Y [#permalink] New post 11 Feb 2008, 09:48
P.S: This is from the PowerPREP test 1. Whats OA? Questions from the Official Guide books?
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Re: Number shortest paths from X to Y [#permalink] New post 11 Feb 2008, 12:24
Anytime I see low answer choices like that I'd count. Took me about 20 secs to do this problem I counted how many ways you could go if you went right then wrote it down and found how many ways you could go if you started up.

I think even if I had done math to get the answer I'd have quickly scanned the picture to make sure it worked. So in this case I skipped the math.
Re: Number shortest paths from X to Y   [#permalink] 11 Feb 2008, 12:24
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Q. Every move up or down is 1 unit. Minimum distance between

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