Last visit was: 17 May 2026, 15:38 It is currently 17 May 2026, 15:38
Home
Messages
Tests
Schools
Events
Close
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
Your Progress

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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
   1   2 
User avatar
MHIKER
User avatar
Joined: 14 Jul 2010
Last visit: 24 May 2021
Posts: 938
Own Kudos:
5,845
Given Kudos: 690
Status:No dream is too large, no dreamer is too small
Concentration: Accounting
Posts: 938
Kudos: 5,845
In the figure above, X and Y represent locations in a district of a ce 06 Mar 2021, 02:56
Kudos
Add Kudos
Bookmarks
Bookmark this Post
gmatt1476

In the figure above, X and Y represent locations in a district of a certain city where the streets form a rectangular grid. In traveling only north or east along the streets from X to Y, how many different paths are possible?

A. 720
B. 512
C. 336
D. 256
E. 56


PS61551.01

Show Spoiler
Attachment:
2019-09-21_1421.png
Show more


There are 3 upwards ways and 5 rightwards ways; Total ways = 5+3=8

The shortest path \(=C^8_3=56\)

The answer is E
avatar
bahruz1992
avatar
Joined: 30 Mar 2020
Last visit: 25 Mar 2022
Posts: 17
Own Kudos:
11
Given Kudos: 34
Posts: 17
Kudos: 11
In the figure above, X and Y represent locations in a district of a ce 12 Sep 2021, 07:57
Kudos
Add Kudos
Bookmarks
Bookmark this Post
GMATinsight
gmatt1476

In the figure above, X and Y represent locations in a district of a certain city where the streets form a rectangular grid. In traveling only north or east along the streets from X to Y, how many different paths are possible?

A. 720
B. 512
C. 336
D. 256
E. 56


PS61551.01

Show Spoiler
Attachment:
2019-09-21_1421.png


ANswer: Option E

GMATinsight's Solution


Get the VIDEO solutions of ALL QUANT problems of "GMAT Official Advanced Questions" here.



Subscribe to my YouTube Channel for FREE resource



Subscribe Topic-wise UN-bundled Video course. CHECK FREE Sample Videos
Show more

Excellent explanation! Thank you.
User avatar
CrackverbalGMAT
User avatar
Major Poster
Joined: 03 Oct 2013
Last visit: 17 May 2026
Posts: 4,849
Own Kudos:
9,206
Given Kudos: 227
Affiliations: CrackVerbal
Location: India
Expert
Expert reply
Posts: 4,849
Kudos: 9,206
In the figure above, X and Y represent locations in a district of a ce 17 Dec 2021, 05:08
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Each possible pathway includes travelling 3 grid segments North and 5 East.

Hence if you look at it the question is asking us the number of permutations of 8 objects that has 3 identical N and 5 identical E.

Number of such arrangement = 8! / (3!5!) = 56

(option e)

D.S
GMAT SME
Attachments

Screenshot (538).png
Screenshot (538).png [ 8.29 KiB | Viewed 3505 times ]

User avatar
BrentGMATPrepNow
User avatar
Major Poster
Joined: 12 Sep 2015
Last visit: 31 Oct 2025
Posts: 6,733
Own Kudos:
36,583
 [3]
Given Kudos: 799
Location: Canada
Expert
Expert reply
Posts: 6,733
Kudos: 36,583
 [3]
In the figure above, X and Y represent locations in a district of a ce 22 Mar 2022, 13:10
2
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
gmatt1476

In the figure above, X and Y represent locations in a district of a certain city where the streets form a rectangular grid. In traveling only north or east along the streets from X to Y, how many different paths are possible?

A. 720
B. 512
C. 336
D. 256
E. 56


PS61551.01

Show Spoiler
Attachment:
2019-09-21_1421.png
Show more

If we define paths from X to Y in a block-by-block manner, we can see that any route from X to Y will consist of 3 NORTHS and 5 EASTS.

For example, this particular path....

... can be defined as ENENEEEN (where E stands for 1 block east, and N stands for 1 block north.

Similarly, this path...

... can be defined as NNENEEEE

So our question becomes, "In how many different ways can we arrange 3 N's and 5 E's?"

-----------ASIDE-----------------
When we want to arrange a group of items in which some of the items are identical, we can use something called the MISSISSIPPI rule. It goes like this:

If there are n objects where A of them are alike, another B of them are alike, another C of them are alike, and so on, then the total number of possible arrangements = n!/[(A!)(B!)(C!)....]

So, for example, we can calculate the number of arrangements of the letters in MISSISSIPPI as follows:
There are 11 letters in total
There are 4 identical I's
There are 4 identical S's
There are 2 identical P's
So, the total number of possible arrangements = 11!/[(4!)(4!)(2!)]
---------------------------------

Now let's apply the MISSISSIPPI rule to arranging 3 N's and 5 E's
There are 8 letters in total
There are 3 identical N's
There are 5 identical E's
So, the total number of possible arrangements = 8!/[(3!)(5!)] = 56

Answer: E

Cheers,
Brent
User avatar
MBAHOUSE
User avatar
MBA House Admissions Consultant
Joined: 26 May 2022
Last visit: 23 Apr 2024
Posts: 337
Own Kudos:
99
Expert
Expert reply
Posts: 337
Kudos: 99
In the figure above, X and Y represent locations in a district of a ce 06 Jun 2022, 13:51
Kudos
Add Kudos
Bookmarks
Bookmark this Post
This is a classic combinatorics question of permutation with repetition where you put the total possibilities factorial in the numerator and the repetitions factorial in the denominator.
You always walk 5 steps to the right and 3 to the top whatever the possibility that you choose.

Permutation of 8 steps with 3 and 5 repetitions.

8!/3!5!= 56

E
User avatar
arbazfatmi1994
User avatar
Joined: 05 Jul 2022
Last visit: 16 Jan 2024
Posts: 102
Own Kudos:
18
Given Kudos: 31
Location: India
WE:Advertising (Healthcare/Pharmaceuticals)
Products:
My Reviews
Posts: 102
Kudos: 18
In the figure above, X and Y represent locations in a district of a ce 12 Aug 2023, 10:08
Kudos
Add Kudos
Bookmarks
Bookmark this Post
This is a really excellent question.

Don't let the diagram frighten you

This question is all about out of the "grid" thinking. ;)

There can be n number of ways to reach point B from A, but all the paths must have 5 east and 3 north

EEEEENNN

So how many ways can be there? As many arrangements are there for the above

8! / 5!*3!
= 56 ways

I hope it helps! :)
User avatar
SPM1234
User avatar
Joined: 20 Mar 2024
Last visit: 30 Jan 2026
Posts: 14
Own Kudos:
23
Given Kudos: 18
Location: India
Posts: 14
Kudos: 23
In the figure above, X and Y represent locations in a district of a ce 02 Jun 2024, 23:06
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Do questions like these (questions related to direction and counting questions that need us to count the number of ways of reaching one point to another) which are in the GMAT Official Advanced questions book(2020) show up in the newer GMAT Focus Edition?
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 17 May 2026
Posts: 110,522
Own Kudos:
815,420
 [1]
Given Kudos: 106,277
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 110,522
Kudos: 815,420
 [1]
In the figure above, X and Y represent locations in a district of a ce 03 Jun 2024, 00:11
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
SPM1234
Do questions like these (questions related to direction and counting questions that need us to count the number of ways of reaching one point to another) which are in the GMAT Official Advanced questions book(2020) show up in the newer GMAT Focus Edition?
Show more
­The short answer would be - yes.
User avatar
Natansha
User avatar
Joined: 13 Jun 2019
Last visit: 11 Mar 2026
Posts: 195
Own Kudos:
65
Given Kudos: 84
Posts: 195
Kudos: 65
In the figure above, X and Y represent locations in a district of a ce 14 Mar 2025, 09:17
Kudos
Add Kudos
Bookmarks
Bookmark this Post
chetan2u
gmatt1476

In the figure above, X and Y represent locations in a district of a certain city where the streets form a rectangular grid. In traveling only north or east along the streets from X to Y, how many different paths are possible?

A. 720
B. 512
C. 336
D. 256
E. 56


PS61551.01

Show Spoiler
Attachment:
2019-09-21_1421.png


If you look at the streets, you have to move 5 streets in the east and 3 streets to the north..

Thus, the total streets are 5+3 and the 3 N or 5 E can be chosen out of these in any order..

So, total ways = 8C3=\(\frac{8!}{5!3!}=\frac{8*7*6}{3*2}=8*7=56\). Hence 56 ways.

E
Show more
Hi, where does the 3 comes in from in 8C3 ?
User avatar
luisdicampo
User avatar
Joined: 10 Feb 2025
Last visit: 30 Apr 2026
Posts: 480
Own Kudos:
81
Given Kudos: 328
Products:
My Reviews
Posts: 480
Kudos: 81
In the figure above, X and Y represent locations in a district of a ce 08 Apr 2026, 01:04
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Deconstructing the Question

To get from X to Y, we can move only east or north.

So the problem becomes: how many ways can we arrange the required east and north moves?

Step-by-step

Count the grid carefully.

There are \(5\) moves east and \(3\) moves north.

So each path has a total of

\(5 + 3 = 8\)

moves.

Now choose where the \(3\) north moves go among the \(8\) total moves:

\(\binom{8}{3}\)

Compute:

\(\binom{8}{3} = \frac{8 \cdot 7 \cdot 6}{3 \cdot 2 \cdot 1} = 56\)

Answer E
   1   2 
Moderators:
Bunuel
Math Expert
110522 posts
Krunaal
Tuck School Moderator
852 posts