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# OG-Question 316-Page 118-Pat goes from intersection X to Y

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Manager
Joined: 14 May 2005
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OG-Question 316-Page 118-Pat goes from intersection X to Y [#permalink]  14 Jun 2005, 13:34
Please refer the question number 316 in Problem Solving section of The Official Guide. For those who do not have the guide, refer the following link.

http://www.gmatclub.com/phpbb/viewtopic.php?t=2165

The Official Guide explains that the answer can be reached by counting the number of routes manually. But that does not sit well within me. I also found that few club members tried to solve the problem using combination formulas. However, there is no sufficient support for the reasoning. Please see: http://www.gmatclub.com/phpbb/viewtopic.php?t=1790

Question:
Is there really an alternative solution available for this problem without counting routes manually? If so, please explain in detail.
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Manager
Joined: 22 Apr 2005
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Manager
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Re: OG-Question 316-Page 118-Pat goes from intersection X to [#permalink]  14 Jun 2005, 15:13
I can just say that a similar question was in my test a year ago. Although there were 10 paths up and 10 to the right > at 9th there were 2 options, etc .. so there were like 200 possibilities, no way you can do it manually
Manager
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Tyr wrote:

Tyr:

Thanks much! I found the solution proposed by Shaq in testmagic forum is interesting.

Michalky, thanks too!
Manager
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I though you were asking about solution not the formula I.e. how do you know given formula always works?
The key here is to rephrase the problem from obscure form given into something mathematical.
You write each solution as a fixed sequence of slots (number of columns/rows) filled up with numbers you get from splitting up number of rows/columns. Then count.
And yes, OG is right. It is much faster to do some counting with elimination because the numbers here are small.
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