Alicia lives in a town whose streets are on a grid system : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 23 Feb 2017, 15:40

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Alicia lives in a town whose streets are on a grid system

Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 23 Mar 2011
Posts: 473
Location: India
GPA: 2.5
WE: Operations (Hospitality and Tourism)
Followers: 20

Kudos [?]: 228 [1] , given: 59

Alicia lives in a town whose streets are on a grid system [#permalink]

### Show Tags

01 Feb 2012, 10:05
1
KUDOS
2
This post was
BOOKMARKED
00:00

Difficulty:

(N/A)

Question Stats:

33% (02:22) correct 67% (01:17) wrong based on 17 sessions

### HideShow timer Statistics

Alicia lives in a town whose streets are on a grid system, with all streets running east-west or north-south without breaks. Her school, located on a corner, lies three blocks south and three blocks east of her home, also located on a corner. If Alicia s equally likely to choose any possible path from home to school, and if she only walks south or east, what is the probability she will walk south for the first two blocks?
_________________

"When the going gets tough, the tough gets going!"

Bring ON SOME KUDOS MATES+++

-----------------------------

My GMAT journey begins: http://gmatclub.com/forum/my-gmat-journey-begins-122251.html

Math Expert
Joined: 02 Sep 2009
Posts: 37102
Followers: 7251

Kudos [?]: 96439 [1] , given: 10751

Re: Alicia lives in a town whose streets are on a grid system [#permalink]

### Show Tags

01 Feb 2012, 10:27
1
KUDOS
Expert's post
7
This post was
BOOKMARKED
sdas wrote:
Alicia lives in a town whose streets are on a grid system, with all streets running east-west or north-south without breaks. Her school, located on a corner, lies three blocks south and three blocks east of her home, also located on a corner. If Alicia s equally likely to choose any possible path from home to school, and if she only walks south or east, what is the probability she will walk south for the first two blocks?

To get to the school Alicia should walk 3 times south and 3 times east: SSSEEE. Total # of routs to the school is # of permutation of SSSEEE, which is 6!/(3!3!)=20 (# of permutations of 6 letters out of which 3 S's and 3 E's are identical);

Now, we wan to count all the routs which start with {SS}. So, {SS} is fixed and then there can be any combination of the rest 4 letters SEEE. So, all possible routs which start with {SS} equal to # of permutation of SEEE, which is 4!/3!=4 (# of permutations of 4 letters out of which 3 E's).

P=4/20=1/5.
_________________
Senior Manager
Joined: 23 Mar 2011
Posts: 473
Location: India
GPA: 2.5
WE: Operations (Hospitality and Tourism)
Followers: 20

Kudos [?]: 228 [0], given: 59

Re: Alicia lives in a town whose streets are on a grid system [#permalink]

### Show Tags

01 Feb 2012, 10:46
Thanks Bunuel: the only part I was making mistake was (SS) to be considered 1 and then SEEE as 4. I was considering it as (SS) = 1 + SEEE (4) total 5. Thats why I was going wrong.
_________________

"When the going gets tough, the tough gets going!"

Bring ON SOME KUDOS MATES+++

-----------------------------

My GMAT journey begins: http://gmatclub.com/forum/my-gmat-journey-begins-122251.html

Intern
Joined: 02 Oct 2012
Posts: 31
WE: Other (Retail Banking)
Followers: 0

Kudos [?]: 6 [0], given: 174

Re: Alicia lives in a town whose streets are on a grid system [#permalink]

### Show Tags

15 Jan 2013, 04:20
Hello,

I have a question to Bunuel. the formula you are using is Combination's formula as it is 6!/(6-3)!*3!, and since Alice has to choose 3 Ss and 3Es, where order does not matter, it has to be Combination. but you are saying that "Total # of routs to the school is # of permutation of SSSEEE, which is 6!/(3!3!)=20 (# of permutations of 6 letters out of which 3 S's and 3 E's are identical)"[u][/u]. can you please explain whether it should be a combination or permutation formula?

I am having hard time understanding this problem. Manhattan guide explains it with anagram grid, but I am not grasping that model. I tried to solve it using Slot Method, but could not do it. I can't really get it with combination/permutation formulas either. can you please explain it in an easier way with more details?
Intern
Joined: 10 Jun 2013
Posts: 4
Followers: 0

Kudos [?]: 3 [0], given: 0

Re: Alicia lives in a town whose streets are on a grid system [#permalink]

### Show Tags

03 Jul 2013, 05:54
A slightly lengthier method would be:

Total number of ways to go home, considering that the order order matters =
Options: SSSEEE
Slots : ------
total permutations of 6 options in 6 slots: 6P6 = 6! = 6*5*4*3*2

Total ways to select "South" in the first 2 positions and anything else in the subsequent 4 positions =
Options: SS ????
Slots: -- ----

Permutations of 3 "S" in 2 slots AND Permutations of 4 Choices in 4 slots =
3P2 * 4P4 = 3! * 4! = 3*2*4*3*2

The probability is therefore:

3P2 * 4P4
--------------- =
6P6

3*2*4*3*2
-------------- = 1/5
6*5*4*3*2
Math Expert
Joined: 02 Sep 2009
Posts: 37102
Followers: 7251

Kudos [?]: 96439 [1] , given: 10751

Re: Alicia lives in a town whose streets are on a grid system [#permalink]

### Show Tags

03 Jul 2013, 06:50
1
KUDOS
Expert's post
sdas wrote:
Alicia lives in a town whose streets are on a grid system, with all streets running east-west or north-south without breaks. Her school, located on a corner, lies three blocks south and three blocks east of her home, also located on a corner. If Alicia s equally likely to choose any possible path from home to school, and if she only walks south or east, what is the probability she will walk south for the first two blocks?

Similar questions to practice:
pat-will-walk-from-intersection-x-to-intersection-y-along-a-104817.html
how-many-ways-are-there-for-3-males-and-3-females-to-sit-106485.html
josh-has-to-run-an-electrical-wire-from-point-a-to-point-b-99962.html
every-morning-casey-walks-from-her-house-to-the-bus-stop-104236.html
_________________
Senior Manager
Joined: 17 Dec 2012
Posts: 447
Location: India
Followers: 26

Kudos [?]: 407 [0], given: 14

Re: Alicia lives in a town whose streets are on a grid system [#permalink]

### Show Tags

03 Jul 2013, 10:23
1. Alicia can choose only the following as the first two in the path: S1 S2, E1 E2, S1 E1 and E1 S1
2. The total number of paths starting with each of the above are 4,4,6 and 6 respectively
3. Therefore the probability that Alicia chooses two south as the first two is 4/20=1/5.
_________________

Srinivasan Vaidyaraman
Sravna
http://www.sravnatestprep.com

Classroom and Online Coaching

Intern
Joined: 15 Aug 2011
Posts: 20
Location: United States
Concentration: Marketing, Technology
GPA: 3.6
WE: Project Management (Computer Software)
Followers: 0

Kudos [?]: 16 [0], given: 53

Re: Alicia lives in a town whose streets are on a grid system [#permalink]

### Show Tags

03 Jul 2013, 13:38
nintso wrote:
Hello,

I have a question to Bunuel. the formula you are using is Combination's formula as it is 6!/(6-3)!*3!, and since Alice has to choose 3 Ss and 3Es, where order does not matter, it has to be Combination. but you are saying that "Total # of routs to the school is # of permutation of SSSEEE, which is 6!/(3!3!)=20 (# of permutations of 6 letters out of which 3 S's and 3 E's are identical)"[u][/u]. can you please explain whether it should be a combination or permutation formula?

I am having hard time understanding this problem. Manhattan guide explains it with anagram grid, but I am not grasping that model. I tried to solve it using Slot Method, but could not do it. I can't really get it with combination/permutation formulas either. can you please explain it in an easier way with more details?

I have two keywords for Permutations and combinations - Arrangement and Selection.

SELECTION means - CHOOSING 1, more or nothing. (Combinations)

ARRANGEMENT means - RE-ORGANIZING or ORDER(Permutations)

In this given problem, Alice should definitely take 3 souths and 3 Easts to reach her school. But in any 'ORDER' of her choice....
==> I need to use Permutations and not combinations formula as I hear the word 'ORDER'

so calculating the total number of permutations = $$6!/3!3!$$= 20

If Alice needs to take 2 Souths first, then the remaining 4 steps - 1 South and 3 Easts can be re-arranged (user Permutations) in = $$4!/3!$$= 4

Probability = $$4/20 = 1/5$$
_________________

"Hit KUDOS if you like my explanation"

Intern
Joined: 30 Nov 2013
Posts: 6
Location: Netherlands
GPA: 3.4
WE: Marketing (Consumer Products)
Followers: 0

Kudos [?]: 7 [0], given: 0

Re: Alicia lives in a town whose streets are on a grid system [#permalink]

### Show Tags

02 Dec 2013, 11:16
if the order does not matter, the solution with combinatorics is correct. however, the question itself is open to argument. route has a totally different meaning - it is more identical to a decision tree rather than a problem where the 3 Ss and 3 Es are identical SSSEEE-. Therefore, Manhattan GMAT should reconsider this question before using it as an example.

nintso wrote:
Hello,

I have a question to Bunuel. the formula you are using is Combination's formula as it is 6!/(6-3)!*3!, and since Alice has to choose 3 Ss and 3Es, where order does not matter, it has to be Combination. but you are saying that "Total # of routs to the school is # of permutation of SSSEEE, which is 6!/(3!3!)=20 (# of permutations of 6 letters out of which 3 S's and 3 E's are identical)"[u][/u]. can you please explain whether it should be a combination or permutation formula?

I am having hard time understanding this problem. Manhattan guide explains it with anagram grid, but I am not grasping that model. I tried to solve it using Slot Method, but could not do it. I can't really get it with combination/permutation formulas either. can you please explain it in an easier way with more details?
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13937
Followers: 589

Kudos [?]: 167 [0], given: 0

Re: Alicia lives in a town whose streets are on a grid system [#permalink]

### Show Tags

24 Feb 2015, 13:34
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.
_________________
Intern
Joined: 13 Dec 2015
Posts: 1
Followers: 0

Kudos [?]: 0 [0], given: 11

Re: Alicia lives in a town whose streets are on a grid system [#permalink]

### Show Tags

17 Jan 2016, 09:05
Hi guys, any one could explain this problem using the Slots method? Thanks in advance
Intern
Joined: 23 Jul 2011
Posts: 18
Location: India
GMAT 1: 740 Q49 V41
Followers: 0

Kudos [?]: 5 [0], given: 11

Re: Alicia lives in a town whose streets are on a grid system [#permalink]

### Show Tags

29 Jun 2016, 04:18
Bunuel wrote:
sdas wrote:
Alicia lives in a town whose streets are on a grid system, with all streets running east-west or north-south without breaks. Her school, located on a corner, lies three blocks south and three blocks east of her home, also located on a corner. If Alicia s equally likely to choose any possible path from home to school, and if she only walks south or east, what is the probability she will walk south for the first two blocks?

To get to the school Alicia should walk 3 times south and 3 times east: SSSEEE. Total # of routs to the school is # of permutation of SSSEEE, which is 6!/(3!3!)=20 (# of permutations of 6 letters out of which 3 S's and 3 E's are identical);

Now, we wan to count all the routs which start with {SS}. So, {SS} is fixed and then there can be any combination of the rest 4 letters SEEE. So, all possible routs which start with {SS} equal to # of permutation of SEEE, which is 4!/3!=4 (# of permutations of 4 letters out of which 3 E's).

P=4/20=1/5.

Quick question - why do we look at the entire series and not just the first two movements?
I.e. For the first two blocks, she can go SE, ES, SS, EE and we want probability of one of these, so 1/4 ?

Please let me know why this is wrong?
Re: Alicia lives in a town whose streets are on a grid system   [#permalink] 29 Jun 2016, 04:18
Similar topics Replies Last post
Similar
Topics:
20 In city A, the streets are aligned in a grid, where the east 10 07 Aug 2012, 08:20
22 If the 4 x 4 grid in the attached picture is filled with the 11 31 Jan 2012, 18:25
1 In city A, the streets are aligned in a grid, where the east 1 19 Jun 2011, 06:56
3 In city A, the streets are aligned in a grid (see attachment 5 21 Mar 2011, 19:13
number system 3 18 Apr 2010, 23:42
Display posts from previous: Sort by