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Pokhran II
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OG-Question 316-Page 118-Pat goes from intersection X to Y 14 Jun 2005, 14:34
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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.

https://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: https://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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Tyr
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OG-Question 316-Page 118-Pat goes from intersection X to Y 14 Jun 2005, 16:02
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Solution was posted here
https://www.gmatclub.com/phpbb/viewtopic ... highlight=
Classic
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michalky
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OG-Question 316-Page 118-Pat goes from intersection X to Y 14 Jun 2005, 16:13
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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
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Pokhran II
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OG-Question 316-Page 118-Pat goes from intersection X to Y 14 Jun 2005, 17:02
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Tyr
Solution was posted here
https://www.gmatclub.com/phpbb/viewtopic ... highlight=
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Tyr:

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

https://www.testmagic.com/forums/showthread.php?t=15550

Let me know your thoughts.

Michalky, thanks too!
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OG-Question 316-Page 118-Pat goes from intersection X to Y 14 Jun 2005, 17:27
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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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