It is currently 20 Oct 2017, 05:50

### 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

# Following are the four regions 1, 2, 3 and 4 and they need to be color

Author Message
TAGS:

### Hide Tags

Intern
Joined: 16 Jan 2011
Posts: 5

Kudos [?]: 11 [0], given: 1

Following are the four regions 1, 2, 3 and 4 and they need to be color [#permalink]

### Show Tags

08 Mar 2011, 18:22
00:00

Difficulty:

(N/A)

Question Stats:

75% (00:24) correct 25% (00:00) wrong based on 5 sessions

### HideShow timer Statistics

Following are the four regions 1, 2, 3 and 4 and they need to be colored with 3 different colors but no two adjacent regions can have same color. For example, region 1, 3 and 4 can be colored with same color and region 2 with a different color. How many such color combination exist with which the region can be colored.

A. 4
B. 6
C. 9
D. 24
E. 36

[Reveal] Spoiler:
Attachment:

untitled.JPG [ 4.8 KiB | Viewed 1295 times ]
[Reveal] Spoiler: OA

Last edited by Bunuel on 16 May 2017, 08:00, edited 2 times in total.
Renamed the topic, edited the question and added the OA.

Kudos [?]: 11 [0], given: 1

Director
Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
Joined: 03 Feb 2011
Posts: 871

Kudos [?]: 396 [0], given: 123

Re: Following are the four regions 1, 2, 3 and 4 and they need to be color [#permalink]

### Show Tags

08 Mar 2011, 18:26
1234
I can choose 4C3 colors and these three colors can be ordered in 3! ways. So 4! combination. The answer has to be more than 4!. Hence I will guess E.

Kudos [?]: 396 [0], given: 123

GMAT Tutor
Joined: 24 Jun 2008
Posts: 1339

Kudos [?]: 1954 [1], given: 6

Re: Following are the four regions 1, 2, 3 and 4 and they need to be color [#permalink]

### Show Tags

08 Mar 2011, 18:50
1
KUDOS
Expert's post
You have:

3 choices for the color of region 1
2 choices for the color of region 2 (must be different from region 1)
2 choices for the color of region 3 (must be different from region 2)
2 choices for the color of region 4 (must be different from region 2)

Multiplying your choices gives 3*2*2*2 = 24 colorings in total.
_________________

GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

Kudos [?]: 1954 [1], given: 6

Director
Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
Joined: 03 Feb 2011
Posts: 871

Kudos [?]: 396 [0], given: 123

Re: Following are the four regions 1, 2, 3 and 4 and they need to be color [#permalink]

### Show Tags

08 Mar 2011, 19:29
thanks Ian - yes I misinterpreted. This question is resisting any straight formulas or formal approach.

IanStewart wrote:
You have:

3 choices for the color of region 1
2 choices for the color of region 2 (must be different from region 1)
2 choices for the color of region 3 (must be different from region 2)
2 choices for the color of region 4 (must be different from region 2)

Multiplying your choices gives 3*2*2*2 = 24 colorings in total.

Kudos [?]: 396 [0], given: 123

Re: Following are the four regions 1, 2, 3 and 4 and they need to be color   [#permalink] 08 Mar 2011, 19:29
Display posts from previous: Sort by