Author 
Message 
TAGS:

Hide Tags

Senior Manager
Joined: 15 Jun 2010
Posts: 332
Schools: IE'14, ISB'14, Kellogg'15
WE 1: 7 Yrs in Automobile (Commercial Vehicle industry)

In city A, the streets are aligned in a grid, where the east
[#permalink]
Show Tags
Updated on: 07 Aug 2012, 13:08
Question Stats:
35% (02:01) correct 65% (02:11) wrong based on 106 sessions
HideShow timer Statistics
Attachment:
Pict.JPG [ 17.67 KiB  Viewed 4457 times ]
In city A, the streets are aligned in a grid, where the eastwest roads are called 1st Rd, 2nd Rd, 3rd Rd, etc, increasing in number as one moves northward. The northsouth roads are called 1st Ave, 2nd Ave, 3rd Ave, etc, increasing in number as one moves eastward. There is a park that runs from 5th Ave to 7th Ave and from 3rd Rd to 5th Rd, as pictured. If Bill needs to walk from the corner of 2nd Rd and 3rd Ave to the corner of 6th Rd and 8th Ave in the shortest possible time without walking through the park, how many different routes could he take? A) 6 B) 66 C) 72 D) 126 E) 262 Is there any formula to find out directly??
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Regards SD  Press Kudos if you like my post. Debrief 610540580710(Long Journey): http://gmatclub.com/forum/from600540580710finallyachievedin4thattempt142456.html
Originally posted by SOURH7WK on 07 Aug 2012, 09:20.
Last edited by SOURH7WK on 07 Aug 2012, 13:08, edited 1 time in total.




Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8195
Location: Pune, India

Re: In city A, the streets are aligned in a grid, where the east
[#permalink]
Show Tags
07 Aug 2012, 23:03
SOURH7WK wrote: In city A, the streets are aligned in a grid, where the eastwest roads are called 1st Rd, 2nd Rd, 3rd Rd, etc, increasing in number as one moves northward. The northsouth roads are called 1st Ave, 2nd Ave, 3rd Ave, etc, increasing in number as one moves eastward. There is a park that runs from 5th Ave to 7th Ave and from 3rd Rd to 5th Rd, as pictured. If Bill needs to walk from the corner of 2nd Rd and 3rd Ave to the corner of 6th Rd and 8th Ave in the shortest possible time without walking through the park, how many different routes could he take?
A) 6 B) 66 C) 72 D) 126 E) 262
Is there any formula to find out directly?? Let me add a little bit of detail to the solution given above. You need to go from a point that is to the bottom left to a point that is to the top right. So you should take steps towards right and top. Since Bill wants to take shortest possible time, he should not go left or down because that is the opposite direction. His destination lies towards right and up. Say, he takes one step to go from one intersection to the next one. He can take various routes e.g. RRRRRUUUU (R represents one step right and U represents one step up) RRRRUUUUR etc The total number of ways is basically obtained by rearranging 5 Rs and 4 Us. You can do it in 9!/5!*4! = 126 ways (we divide by 5! and 4! because all Rs and all Us are identical) Now, what happens due to the park? Everything is the same except that one intersection is not available  4th Rd, 6th Ave. You cannot include this intersection in your journey. So what do you do? You remove all paths that include this intersection. Now our question is this: In how many ways can you go from the corner of 2nd Rd and 3rd Ave to the corner of 6th Rd and 8th Ave when you include the corner of 4th Rd, 6th Ave? From the corner of 2nd Rd and 3rd Ave to the corner of 4th Rd and 6th Ave  You need to take 3 steps right and 2 steps up  RRRUU etc. No of ways = 5!/3!*2! = 10 From the corner of 4th Rd and 6th Ave to the corner of 6th Rd and 8th Ave  You need to take 2 steps right and 2 steps up  RRUU etc. No of ways = 4!/2!*2! = 6 Total number of ways in which the 4th Rd, 6th Ave is included = 10*6 = 60 ways Number of paths in which the corner of 4th Rd, 6th Ave is not included = 126  60 = 66
_________________
Karishma Veritas Prep GMAT Instructor
Save up to $1,000 on GMAT prep through 8/20! Learn more here >
GMAT selfstudy has never been more personalized or more fun. Try ORION Free!




Director
Joined: 22 Mar 2011
Posts: 604
WE: Science (Education)

Re: In city A, the streets are aligned in a grid, where the east
[#permalink]
Show Tags
07 Aug 2012, 12:55
SOURH7WK wrote: In city A, the streets are aligned in a grid, where the eastwest roads are called 1st Rd, 2nd Rd, 3rd Rd, etc, increasing in number as one moves northward. The northsouth roads are called 1st Ave, 2nd Ave, 3rd Ave, etc, increasing in number as one moves eastward. There is a park that runs from 5th Ave to 7th Ave and from 3rd Rd to 5th Rd, as pictured. If Bill needs to walk from the corner of 2nd Rd and 3rd Ave to the corner of 6th Rd and 8th Ave in the shortest possible time without walking through the park, how many different routes could he take?
A) 6 B) 66 C) 72 D) 126 E) 262
Is there any formula to find out directly?? Really don't know of any formula that could help... Pretty cruel, definitely not a real GMAT test question. The best I could come up with is as follows: Each optimal path (of minimal length) would consist of 5 walks to the right (R) and 4 walks up (U). The total number of such paths is given by \(9C4=\frac{9*8*7*6}{2*3*4}=126.\) We have to eliminate those optimal paths that go through the center of the park (the intersection between 4th Road and 6th Avenue). He can still walk around the park. To reach the center of the park we need 3R and 2U walks  a total of 5C2=5*4/2=10 possibilities. From the center of the park, to reach the final destination we need 2R and 2U walks  another 4C2=4*3/2=6 possibilities. This would give 10*6=60 paths to eliminate, leaving 12660=66 possibilities. Answer B (not C). Are you sure OA is C?
_________________
PhD in Applied Mathematics Love GMAT Quant questions and running.



Senior Manager
Joined: 15 Jun 2010
Posts: 332
Schools: IE'14, ISB'14, Kellogg'15
WE 1: 7 Yrs in Automobile (Commercial Vehicle industry)

Re: In city A, the streets are aligned in a grid, where the east
[#permalink]
Show Tags
Updated on: 07 Aug 2012, 13:19
Sorry!! U are correct Ans is (B) 66. I have edited the Answer. thank U very much. Can u explain the logic of that 60 ways that u subtracted.
_________________
Regards SD  Press Kudos if you like my post. Debrief 610540580710(Long Journey): http://gmatclub.com/forum/from600540580710finallyachievedin4thattempt142456.html
Originally posted by SOURH7WK on 07 Aug 2012, 13:11.
Last edited by SOURH7WK on 07 Aug 2012, 13:19, edited 1 time in total.



Senior Manager
Joined: 15 Jun 2010
Posts: 332
Schools: IE'14, ISB'14, Kellogg'15
WE 1: 7 Yrs in Automobile (Commercial Vehicle industry)

Re: In city A, the streets are aligned in a grid, where the east
[#permalink]
Show Tags
07 Aug 2012, 13:16
By the way OE provided as per source is below: Draw a grid representing the problem. At every intersection of 2 lines, put the number representing how many possible ways it is to get to that intersection while walking only north and east. There's only one way of walking straight north up the most westerly avenue, so put ones all along that path. Same for the direct east path. Once the first rows, updown and leftright, have been filled in, you can work on the internal intersections. For each intersection, add the numbers found at the intersections to the west and south of it. Since there are such and such many ways to get to the two intersections one spot away from this intersection, adding them together provides the total number of ways to get to that intersection. See below, filled in for this particular question, yielding the answer 66 possible shortest routes.
Attachments
Exp.JPG [ 20.62 KiB  Viewed 4318 times ]
_________________
Regards SD  Press Kudos if you like my post. Debrief 610540580710(Long Journey): http://gmatclub.com/forum/from600540580710finallyachievedin4thattempt142456.html



Director
Joined: 22 Mar 2011
Posts: 604
WE: Science (Education)

Re: In city A, the streets are aligned in a grid, where the east
[#permalink]
Show Tags
07 Aug 2012, 13:57
SOURH7WK wrote: Sorry!! U are correct Ans is (B) 66. I have edited the Answer. thank U very much.
Can u explain the logic of that 60 ways that u subtracted. Did you understand the way I got the total number of paths 126? The 60 is similar, but because each path has to go through the center of the park, I had to split each such path into two: from start to the center of the park and then, from the center to destination. So, it will be (the number of ways to reach the center) * (the number of ways to go from the center to destination). First path is of type 3R and 2U, the second path is 2R and 2U. Therefore, (5*4/2) * (4*3/2) = 60. For example, for the first path, which is composed of 3 right walks and 2 up walks, the sequence is of length 5 (walks). I just have to decide out of the 5 walks, when to go up, the other three I will certainly go to the right. This is given by 5C2 = 10. This you can even check, the list is not sooo long: UURRR RUURR RRUUR RRRUU URURR URRUR URRRU RURUR RURRU RRURU But it is important to understand how each path is built, and the number of choices. Then, use the appropriate formulas.
_________________
PhD in Applied Mathematics Love GMAT Quant questions and running.



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8195
Location: Pune, India

Re: In city A, the streets are aligned in a grid, where the east
[#permalink]
Show Tags
07 Aug 2012, 23:05
P.S.  Didn't see you have already posted the explanation...
_________________
Karishma Veritas Prep GMAT Instructor
Save up to $1,000 on GMAT prep through 8/20! Learn more here >
GMAT selfstudy has never been more personalized or more fun. Try ORION Free!



Math Expert
Joined: 02 Sep 2009
Posts: 48037

Re: In city A, the streets are aligned in a grid, where the east
[#permalink]
Show Tags
08 Aug 2012, 01:00



Director
Status: Everyone is a leader. Just stop listening to others.
Joined: 22 Mar 2013
Posts: 871
Location: India
GPA: 3.51
WE: Information Technology (Computer Software)

Re: In city A, the streets are aligned in a grid, where the east
[#permalink]
Show Tags
21 Jul 2013, 14:21
Center of the park is much important in this problem. To pass through the park one must have to pass through this point and further to destination. Ans = Total possible paths to destination(TPPD)  paths passing through the park (PPTP) All possible paths covering min distance are permutation of pattern RRRRRUUUU R> One step right / U> One step up Thus TPPD = 9!/(5!x4!) = 126 (direct formula of permutation applied) I have calculated PPTD in two steps first find all paths from origin to center of park: 1. Possible moves RRRUU total permutations 5!/(3!x2!) = 10 2. From park center to destination, in moves RRUU, total permutations as 4!/(2!x2!)=6. Thus PPTD= 10 X 6 = 60 Ans = 126 60 = 66 Refer following image to understand the logic. Attachment:
Park.jpg [ 63.05 KiB  Viewed 3565 times ]
_________________
Piyush K
 Our greatest weakness lies in giving up. The most certain way to succeed is to try just one more time. ― Thomas A. Edison Don't forget to press> Kudos My Articles: 1. WOULD: when to use?  2. All GMATPrep RCs (New) Tip: Before exam a week earlier don't forget to exhaust all gmatprep problems specially for "sentence correction".



NonHuman User
Joined: 09 Sep 2013
Posts: 7773

Re: In city A, the streets are aligned in a grid, where the east
[#permalink]
Show Tags
27 Oct 2017, 03:48
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). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: In city A, the streets are aligned in a grid, where the east &nbs
[#permalink]
27 Oct 2017, 03:48






