Pat has to walk..

This topic has expert replies
User avatar
Senior | Next Rank: 100 Posts
Posts: 35
Joined: 31 Jul 2011
Thanked: 2 times
Followed by:1 members

Pat has to walk..

by Elena89 » Tue Dec 13, 2011 5:57 am
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

[spoiler]OA: C[/spoiler]
Source: OG-12

Can anyone suggest an easy way to solve this problem and others of such kind?
Attachments
combinatorics.JPG

User avatar
Legendary Member
Posts: 504
Joined: 19 Apr 2011
Thanked: 114 times
Followed by:11 members

by knight247 » Tue Dec 13, 2011 6:35 am
Hey Elena
All the streets and avenues are of equal length hence any route he takes will be of equal length. Its best to use the anagram method for such grid problems.

Suppose he decides the take the extreme route along the outer boundary of the grid...He has to walk
East East and then North North North. Try any random combination by urself and u'll find that every combo has two Easts and 3 Norths. So we have EENNN for short. Which can be permuted in 5!/(3!2!)=
10 Ways Hence C

User avatar
GMAT Instructor
Posts: 15533
Joined: 25 May 2010
Location: New York, NY
Thanked: 13060 times
Followed by:1901 members
GMAT Score:790

by GMATGuruNY » Tue Dec 13, 2011 6:46 am
Elena89 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

[spoiler]OA: C[/spoiler]
Source: OG-12

Can anyone suggest an easy way to solve this problem and others of such kind?
I posted a solution here:

https://www.beatthegmat.com/pat-and-his- ... cityevent=

Two similar problems:

https://www.beatthegmat.com/combinatroni ... 68412.html

https://www.beatthegmat.com/different-routes-t93698.html
Mitch Hunt
Private Tutor for the GMAT and GRE
[email protected]

If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon.

Available for tutoring in NYC and long-distance.
For more information, please email me at [email protected].
Student Review #1
Student Review #2
Student Review #3