Finding Paths

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wilderness: Master | Next Rank: 500 Posts; Posts: 102; Joined: Sat Mar 15, 2008 4:03 am; Thanked: 4 times

by wilderness » Fri Jul 18, 2008 1:38 pm

Hi,

Does anyone have any general formula how to attack a problem like this. I solved it by counting each of the possible shortest ways. But of course if there had been 10 streets and 20 avenues my method would not be useful. I have a feeling that it has got something to do with combinations but I have no further idea. What do you think

The right answer is 10.

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Source: Beat The GMAT — Problem Solving | Fri Jul 18, 2008 1:38 pm

parallel_chase: Legendary Member; Posts: 1153; Joined: Wed Jun 20, 2007 6:21 amFollowed by: 2 members; Thanked: 146 times

Re: Finding Paths

by parallel_chase » Fri Jul 18, 2008 3:16 pm

wilderness wrote:Hi,

Does anyone have any general formula how to attack a problem like this. I solved it by counting each of the possible shortest ways. But of course if there had been 10 streets and 20 avenues my method would not be useful. I have a feeling that it has got something to do with combinations but I have no further idea. What do you think

The right answer is 10.

No matter which route X take to get to Y, X will have to cross 2 avenues and 3 streets.

No. of ways X can take to get to Y = 5!
No. of ways X can cross avenues = 2!
No. of ways X can cross streets = 3!

Therefore 5! / (2! 3!) => 10

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asigheartau: Junior | Next Rank: 30 Posts; Posts: 18; Joined: Sun Jun 22, 2008 11:25 am; Location: NY; Thanked: 1 times

Re: Finding Paths

by asigheartau » Fri Jul 18, 2008 7:56 pm

parallel_chase wrote:
wilderness wrote:
No. of ways X can take to get to Y = 5!

How do you determine that?

Alin Sigheartau

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GMAT/MBA Expert

Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

by Ian Stewart » Sat Jul 19, 2008 12:14 am

See solution here:

www.beatthegmat.com/og-195-197-unsolved ... 12321.html

Yes, it can be solved for any size of grid.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com

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