OG11-Q195

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RM: Senior | Next Rank: 100 Posts; Posts: 47; Joined: Sat Jun 16, 2007 10:58 pm

by RM » Fri Jul 06, 2007 3:43 pm

Pat will walk from intersection X to intersection Y along a route that is confined to the square grid of four streets and three avenues shown in the map. How many routes from X to Y can Pat take that have the minimum possible length?

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Source: Beat The GMAT — Problem Solving | Fri Jul 06, 2007 3:43 pm

givemeanid: Master | Next Rank: 500 Posts; Posts: 277; Joined: Sun Jun 17, 2007 2:51 pmFollowed by: 1 member; Location: New York, NY; Thanked: 6 times

by givemeanid » Fri Jul 06, 2007 4:11 pm

He goes up 3 times and moves right 2 times. Just by counting, I seem to be getting 10. What is OA?

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RM: Senior | Next Rank: 100 Posts; Posts: 47; Joined: Sat Jun 16, 2007 10:58 pm

OA is 10

by RM » Fri Jul 06, 2007 4:49 pm

yeah the answer is 10. I was wondering if there is any mathematical way apart from counting to arrive at the solution.

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givemeanid: Master | Next Rank: 500 Posts; Posts: 277; Joined: Sun Jun 17, 2007 2:51 pmFollowed by: 1 member; Location: New York, NY; Thanked: 6 times

by givemeanid » Fri Jul 06, 2007 5:01 pm

Yes there is.

We essentially need a 5 letter word which will denote the path. The letters in the word should be R, R, U, U, U. The order matters and Rs and Us are indistinguishable.

To find the number of distinct permutations of a set of items with indistinguishable items, divide the factorial of the items in the set by the product of the factorials of the number of indistinguishable elements.

That is 5! / (2! * 3!) = 10.

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discreet: Senior | Next Rank: 100 Posts; Posts: 69; Joined: Wed Apr 25, 2007 1:38 amFollowed by: 1 member

General Concept

by discreet » Fri Jul 06, 2007 11:17 pm

Again,To all my dear members,Here's a general concept that can be used for such type of questions.

I firmly believe that one must always attack the concept first rather than attacking a specific question.So,when I saw this problem,I started searching for a concept that I can use for this problem.

So,here it is : Refer image

This is a part of my personal Flashcards, sharing it now

There's one more similar problem : distance between 2 cities PS pblm...but that's a simpler one that can be easily deduced.

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manu singhal: Newbie | Next Rank: 10 Posts; Posts: 2; Joined: Sat Jun 30, 2007 7:13 pm; Location: NY

can you walk us through the formula for this?

by manu singhal » Sat Jul 28, 2007 2:51 pm

What are th number of the bottom right of C imply mathematically?

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