It is currently 19 Nov 2017, 09:21

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.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

A retail company needs to set up five additional distribution centers

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42249

Kudos [?]: 132696 [1], given: 12335

A retail company needs to set up five additional distribution centers [#permalink]

Show Tags

New post 20 Jan 2015, 06:38
1
This post received
KUDOS
Expert's post
6
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

76% (01:17) correct 25% (01:47) wrong based on 200 sessions

HideShow timer Statistics

A retail company needs to set up five additional distribution centers that can be located in three cities on the east coast (Boston, New York, and Washington, D.C.), one city in the Midwest (Chicago), and three cities on the west coast (Seattle, San Francisco, and Los Angeles). If the company must add two distribution centers on each coast and one in the Midwest, and only one center can be added in each city, in how many ways can the management allocate the distribution centers?

A. 3
B. 9
C. 18
D. 20
E. 36

Kudos for a correct solution.
[Reveal] Spoiler: OA

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 132696 [1], given: 12335

Senior RC Moderator
User avatar
P
Status: It always seems impossible until it's done!!
Joined: 29 Aug 2012
Posts: 1047

Kudos [?]: 1529 [0], given: 277

Location: India
GMAT 1: 680 Q47 V34
WE: General Management (Aerospace and Defense)
GMAT ToolKit User Premium Member Reviews Badge CAT Tests
Re: A retail company needs to set up five additional distribution centers [#permalink]

Show Tags

New post 20 Jan 2015, 23:03
2
This post was
BOOKMARKED
Bunuel wrote:
A retail company needs to set up five additional distribution centers that can be located in three cities on the east coast (Boston, New York, and Washington, D.C.), one city in the Midwest (Chicago), and three cities on the west coast (Seattle, San Francisco, and Los Angeles). If the company must add two distribution centers on each coast and one in the Midwest, and only one center can be added in each city, in how many ways can the management allocate the distribution centers?

A. 3
B. 9
C. 18
D. 20
E. 36

Kudos for a correct solution.


2 distributors in east coast and 2 in west coast. And 1 in Midwest.

So,

East Coast= 3C2: \(\frac{3!}{2!1!}\)= 3.

West Coast= 3C2: \(\frac{3!}{2!1!}\)= 3.

Midwest= 1C1= 1

So The total number of ways will be,

\(3*1*3= 9\).

Answer is B.
_________________

Become a GMAT Club Premium member to avail lot of discounts

Kudos [?]: 1529 [0], given: 277

Manager
Manager
avatar
Joined: 23 Jan 2013
Posts: 172

Kudos [?]: 58 [0], given: 41

Concentration: Technology, Other
Schools: Haas
GMAT Date: 01-14-2015
WE: Information Technology (Computer Software)
GMAT ToolKit User
Re: A retail company needs to set up five additional distribution centers [#permalink]

Show Tags

New post 08 Feb 2015, 03:00
1) There are 3 cities on the East Coast; we must put a distribution center in 2 of them.
2) There is 1 city in the Midwest; we must put a distribution center there.
3) There are 3 cities on the West Coast; we must put a distribution center in 2 of them.

Since the "order" of the distribution centers does NOT matter, we're dealing with a Combinations situation.

East Coast: 3c2 = 3!/[2!1!] = 3 ways to place the distribution centers
Midwest: 1c1 = 1 way to place the distribution center
West Coast: 3c2 = 3!/[2!1!] = 3 ways to place the distribution centers

We have to multiply these results to calculate the TOTAL possible combinations of distribution centers:

(3)(1)(3) = 9 different ways to place the distribution centers.

Kudos [?]: 58 [0], given: 41

Expert Post
Math Expert
User avatar
P
Joined: 02 Aug 2009
Posts: 5210

Kudos [?]: 5842 [0], given: 117

Re: A retail company needs to set up five additional distribution centers [#permalink]

Show Tags

New post 08 Feb 2015, 03:15
Bunuel wrote:
A retail company needs to set up five additional distribution centers that can be located in three cities on the east coast (Boston, New York, and Washington, D.C.), one city in the Midwest (Chicago), and three cities on the west coast (Seattle, San Francisco, and Los Angeles). If the company must add two distribution centers on each coast and one in the Midwest, and only one center can be added in each city, in how many ways can the management allocate the distribution centers?

A. 3
B. 9
C. 18
D. 20
E. 36

Kudos for a correct solution.

in west coast 2out of 3
in east coast 2out of 3
and mid west 1 of 1..
total ways 3c2*3c2*1c1=9.. ans B
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Kudos [?]: 5842 [0], given: 117

Intern
Intern
avatar
Joined: 27 Apr 2015
Posts: 13

Kudos [?]: 1 [0], given: 114

Location: India
Concentration: Technology, Marketing
Schools: ISB '18 (A)
GMAT 1: 740 Q50 V39
GPA: 3.2
Re: A retail company needs to set up five additional distribution centers [#permalink]

Show Tags

New post 06 Apr 2016, 01:35
Cant we have 3 on east coast and only one on the west.



chetan2u wrote:
Bunuel wrote:
A retail company needs to set up five additional distribution centers that can be located in three cities on the east coast (Boston, New York, and Washington, D.C.), one city in the Midwest (Chicago), and three cities on the west coast (Seattle, San Francisco, and Los Angeles). If the company must add two distribution centers on each coast and one in the Midwest, and only one center can be added in each city, in how many ways can the management allocate the distribution centers?

A. 3
B. 9
C. 18
D. 20
E. 36

Kudos for a correct solution.

in west coast 2out of 3
in east coast 2out of 3
and mid west 1 of 1..
total ways 3c2*3c2*1c1=9.. ans B

Kudos [?]: 1 [0], given: 114

Expert Post
Math Expert
User avatar
P
Joined: 02 Aug 2009
Posts: 5210

Kudos [?]: 5842 [0], given: 117

Re: A retail company needs to set up five additional distribution centers [#permalink]

Show Tags

New post 06 Apr 2016, 01:55
shravanthim wrote:
Cant we have 3 on east coast and only one on the west.



chetan2u wrote:
Bunuel wrote:
A retail company needs to set up five additional distribution centers that can be located in three cities on the east coast (Boston, New York, and Washington, D.C.), one city in the Midwest (Chicago), and three cities on the west coast (Seattle, San Francisco, and Los Angeles). If the company must add two distribution centers on each coast and one in the Midwest, and only one center can be added in each city, in how many ways can the management allocate the distribution centers?

A. 3
B. 9
C. 18
D. 20
E. 36

Kudos for a correct solution.

in west coast 2out of 3
in east coast 2out of 3
and mid west 1 of 1..
total ways 3c2*3c2*1c1=9.. ans B


Hi,
NO, we have to choose two in each coast since it is given the coast..
Quote:
If the company must add two distribution centers on each coast and one in the Midwest,
..

had the wordings been ..
If the company must add one distribution centers in the Midwest, and only one center can be added in each city, in how many ways can the management allocate the distribution centers?
in that case the WAY mentioned by you will also come into play..


Hope it helped
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Kudos [?]: 5842 [0], given: 117

Retired Moderator
User avatar
S
Joined: 18 Sep 2014
Posts: 1201

Kudos [?]: 894 [0], given: 75

Location: India
GMAT ToolKit User Premium Member Reviews Badge
Re: A retail company needs to set up five additional distribution centers [#permalink]

Show Tags

New post 12 Jul 2016, 05:03
chetan2u wrote:
shravanthim wrote:
Cant we have 3 on east coast and only one on the west.
chetan2u wrote:
in west coast 2out of 3
in east coast 2out of 3
and mid west 1 of 1..
total ways 3c2*3c2*1c1=9.. ans B


Hi,
NO, we have to choose two in each coast since it is given the coast..
Quote:
If the company must add two distribution centers on each coast and one in the Midwest,
..

had the wordings been ..
If the company must add one distribution centers in the Midwest, and only one center can be added in each city, in how many ways can the management allocate the distribution centers?
in that case the WAY mentioned by you will also come into play..


Hope it helped


Hi chetan2u

can you elaborate? I have a similar doubt. We need to pick two centers in each coast as per the question.
I think as below
1st distribution center in east coast can have 3 choices
2nd distribution center in east coast can have 2 choices
Similar case with west coast.
Whats wrong with my thinking?
_________________

The only time you can lose is when you give up. Try hard and you will suceed.
Thanks = Kudos. Kudos are appreciated

http://gmatclub.com/forum/rules-for-posting-in-verbal-gmat-forum-134642.html
When you post a question Pls. Provide its source & TAG your questions
Avoid posting from unreliable sources.


My posts
http://gmatclub.com/forum/beauty-of-coordinate-geometry-213760.html#p1649924
http://gmatclub.com/forum/calling-all-march-april-gmat-takers-who-want-to-cross-213154.html
http://gmatclub.com/forum/possessive-pronouns-200496.html
http://gmatclub.com/forum/double-negatives-206717.html
http://gmatclub.com/forum/the-greatest-integer-function-223595.html#p1721773
https://gmatclub.com/forum/improve-reading-habit-233410.html#p1802265

Kudos [?]: 894 [0], given: 75

Intern
Intern
avatar
Joined: 19 Feb 2013
Posts: 3

Kudos [?]: 5 [0], given: 81

Location: India
GMAT 1: 610 Q43 V31
Reviews Badge
Re: A retail company needs to set up five additional distribution centers [#permalink]

Show Tags

New post 14 Jul 2016, 04:48
I solved this question the same way:

East Coast : 3x2 (and) West Coast: 3x2 (and) Midwest 1 = 36

Please do point out the error in this logic.

Regards,
Arvind.

Kudos [?]: 5 [0], given: 81

Intern
Intern
avatar
Joined: 08 Mar 2016
Posts: 14

Kudos [?]: 3 [0], given: 6

GMAT ToolKit User
Re: A retail company needs to set up five additional distribution centers [#permalink]

Show Tags

New post 21 Jul 2016, 13:21
ASredhar wrote:
I solved this question the same way:

East Coast : 3x2 (and) West Coast: 3x2 (and) Midwest 1 = 36

Please do point out the error in this logic.

Regards,
Arvind.


This way you are considering that the order of the cities in each coast matters, when it actually doesn't.

It doesn't matter if your picks are:

NY Boston Chicago LA SF

or

Boston NY Chicago LA SF

The cities picked are still the same.

Kudos [?]: 3 [0], given: 6

Senior Manager
Senior Manager
User avatar
G
Status: You have to have the darkness for the dawn to come
Joined: 09 Nov 2012
Posts: 319

Kudos [?]: 219 [0], given: 159

Daboo: Sonu
GMAT 1: 590 Q49 V20
GMAT 2: 730 Q50 V38
GMAT ToolKit User Reviews Badge
Re: A retail company needs to set up five additional distribution centers [#permalink]

Show Tags

New post 02 Apr 2017, 10:58
1
This post was
BOOKMARKED
Bunuel wrote:
A retail company needs to set up five additional distribution centers that can be located in three cities on the east coast (Boston, New York, and Washington, D.C.), one city in the Midwest (Chicago), and three cities on the west coast (Seattle, San Francisco, and Los Angeles). If the company must add two distribution centers on each coast and one in the Midwest, and only one center can be added in each city, in how many ways can the management allocate the distribution centers?

A. 3
B. 9
C. 18
D. 20
E. 36

Kudos for a correct solution.


In east coast 3C2 ways..................1
In west coast 3C2 ways..................2
In midwest 1C1 ways ...................3
total= 1*2*3
=9
hence B
_________________

You have to have the darkness for the dawn to come.

Give Kudos if you like my post

Kudos [?]: 219 [0], given: 159

Manager
Manager
avatar
S
Joined: 08 Oct 2016
Posts: 191

Kudos [?]: 19 [0], given: 75

Location: United States
Concentration: General Management, Finance
GPA: 2.9
WE: Engineering (Telecommunications)
Re: A retail company needs to set up five additional distribution centers [#permalink]

Show Tags

New post 15 Apr 2017, 02:47
Answer is B.. Get is 1:24 should be less though
East coast*Mid coast*west coast
3c2*1c1*3c2
3*1*3
9
_________________

Got Q42,V17
Target#01 Q45,V20--April End

Kudos [?]: 19 [0], given: 75

Intern
Intern
avatar
B
Joined: 01 Feb 2017
Posts: 43

Kudos [?]: 18 [0], given: 19

CAT Tests
Re: A retail company needs to set up five additional distribution centers [#permalink]

Show Tags

New post 17 Apr 2017, 14:07
There are 5 Centres and 7 Cities ( EC:3, WC:3, MW:1).
Constraints: 2 Centres affixed to EC; 2 Centres affixed to WC ; 1 Centre affixed to MW.
Ways to Distribute Centres: MW- 1 ; EC: 3C2 ; WC: 3C2.
Hence, Total ways= MW x EC x WC = 1 × 3 × 3 = 9.
Correct Choice: B

Kudos [?]: 18 [0], given: 19

Director
Director
avatar
S
Joined: 12 Nov 2016
Posts: 794

Kudos [?]: 36 [0], given: 165

Re: A retail company needs to set up five additional distribution centers [#permalink]

Show Tags

New post 22 Apr 2017, 00:36
Bunuel wrote:
A retail company needs to set up five additional distribution centers that can be located in three cities on the east coast (Boston, New York, and Washington, D.C.), one city in the Midwest (Chicago), and three cities on the west coast (Seattle, San Francisco, and Los Angeles). If the company must add two distribution centers on each coast and one in the Midwest, and only one center can be added in each city, in how many ways can the management allocate the distribution centers?

A. 3
B. 9
C. 18
D. 20
E. 36

Kudos for a correct solution.


We don't necessarily need to factor in the midwest city since there is only one possibility for it; now, actually, the most logical way to think of the problem is that there are three cities that will have or rather choose 2 cities among the 4 cities remaining instead of thinking 4 cities choose 2 spots-

3c2 x 3c2 = 9

Kudos [?]: 36 [0], given: 165

Intern
Intern
avatar
B
Joined: 05 Oct 2014
Posts: 24

Kudos [?]: 12 [0], given: 88

Concentration: Finance, Entrepreneurship
GMAT ToolKit User CAT Tests
Re: A retail company needs to set up five additional distribution centers [#permalink]

Show Tags

New post 17 Sep 2017, 04:50
The management allocate the distribution centers in : 3C2 * 1C1 * 3C2 = 9

the answer is option B.

Bunuel : please provide the OA after review.

Kudos [?]: 12 [0], given: 88

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42249

Kudos [?]: 132696 [0], given: 12335

Re: A retail company needs to set up five additional distribution centers [#permalink]

Show Tags

New post 17 Sep 2017, 04:55

Kudos [?]: 132696 [0], given: 12335

Chat Moderator
avatar
G
Joined: 04 Aug 2016
Posts: 589

Kudos [?]: 92 [0], given: 140

Location: India
Concentration: Leadership, Strategy
GPA: 4
WE: Engineering (Telecommunications)
Premium Member CAT Tests
A retail company needs to set up five additional distribution centers [#permalink]

Show Tags

New post 17 Sep 2017, 05:10
Nevernevergiveup wrote:

Hi chetan2u

can you elaborate? I have a similar doubt. We need to pick two centers in each coast as per the question.
I think as below
1st distribution center in east coast can have 3 choices
2nd distribution center in east coast can have 2 choices
Similar case with west coast.
Whats wrong with my thinking?


Hi Nevernevergiveup,

If i understood correctly, you would also need to divide by 2! in order to account for any false counts i.e. duplicates. So you would end with 3 such cases per coast.

Kudos [?]: 92 [0], given: 140

A retail company needs to set up five additional distribution centers   [#permalink] 17 Sep 2017, 05:10
Display posts from previous: Sort by

A retail company needs to set up five additional distribution centers

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.