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# Pat will walk from intersection X to intersection Y along a route that

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Intern
Joined: 05 Oct 2009
Posts: 25
Pat will walk from intersection X to intersection Y along a route that  [#permalink]

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14 Nov 2010, 08:55
4
21
00:00

Difficulty:

55% (hard)

Question Stats:

59% (01:38) correct 41% (01:59) wrong based on 269 sessions

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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 above. How many routes from X to Y can Pat take that have the minimum possible length?

A. 6
B. 8
C. 10
D. 14
E. 16

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Q.png [ 25.04 KiB | Viewed 5200 times ]

Attachment:

Untitled.png [ 5.67 KiB | Viewed 2042 times ]
Math Expert
Joined: 02 Sep 2009
Posts: 53831
Pat will walk from intersection X to intersection Y along a route that  [#permalink]

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14 Nov 2010, 09:09
10
6
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 above. How many routes from X to Y can Pat take that have the minimum possible length?

A) 6
B) 8
C) 10
D) 14
E) 16

In order the length to be minimum Pat should only go UP and RIGHT: namely thrice UP and twice RIGHT.

So combination of UUURR: # of permutations of 5 letters out of which there are 3 identical U's and 2 identical R's is 5!/(3!2!) = 10.

Similar questions:
http://gmatclub.com/forum/grockit-simil ... re#p770816
http://gmatclub.com/forum/casey-and-the ... te#p812794

Hope it's clear.
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Joined: 16 Oct 2010
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Location: United States
Concentration: Finance, Entrepreneurship
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Re: Pat will walk from intersection X to intersection Y along a route that  [#permalink]

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14 Nov 2010, 09:16
as usual...awesome solution!

+1
Intern
Joined: 05 Oct 2009
Posts: 25
Re: Pat will walk from intersection X to intersection Y along a route that  [#permalink]

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14 Nov 2010, 13:38
Cool solution...

Thanks Bunuel. +1
Intern
Joined: 25 Jan 2018
Posts: 4
Re: Pat will walk from intersection X to intersection Y along a route that  [#permalink]

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04 Mar 2018, 09:38
Hi I don’t understand why we are applying the combination formula instead of the permutation formula. Since we are going thrice up and twice right, and since there are many different ways to go thrice up and twice right, I thought that the order matters, in which case we should apply the permutation formula, no? Can someone explain to me please? Thank you!

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Math Expert
Joined: 02 Sep 2009
Posts: 53831
Re: Pat will walk from intersection X to intersection Y along a route that  [#permalink]

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04 Mar 2018, 09:43
Rurugu wrote:
Hi I don’t understand why we are applying the combination formula instead of the permutation formula. Since we are going thrice up and twice right, and since there are many different ways to go thrice up and twice right, I thought that the order matters, in which case we should apply the permutation formula, no? Can someone explain to me please? Thank you!

Sent from my iPhone using GMAT Club Forum

We ARE taking into account the number of ways UUURR ca=ould be arranged: So combination of UUURR: # of permutations of 5 letters out of which there are 3 identical U's and 2 identical R's is 5!/(3!2!) = 10.
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Re: Pat will walk from intersection X to intersection Y along a route that  [#permalink]

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04 Mar 2018, 10:21
1
1
gmatexam2009 wrote:

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 above. How many routes from X to Y can Pat take that have the minimum possible length?

A. 6
B. 8
C. 10
D. 14
E. 16

Attachment:
Q.png

Attachment:
Untitled.png

No matter which path he takes, Pat must take 3 Ups and 2 Rights. It is the same as arranging a 5 lettered word, with 3 Us and 2Rs. Hence 5C3.

To generalise, if there are m rows and n columns, the number of paths would be (m+n)Cm or (m+n)Cn.
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Re: Pat will walk from intersection X to intersection Y along a route that  [#permalink]

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14 Mar 2019, 03:29
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Pat will walk from intersection X to intersection Y along a route that   [#permalink] 14 Mar 2019, 03:29
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