GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 15 Jul 2018, 23:34

### 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

# John has 12 clients and he wants to use color coding to

Author Message
Manager
Joined: 04 Jun 2008
Posts: 141
John has 12 clients and he wants to use color coding to [#permalink]

### Show Tags

26 Aug 2008, 17:27
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 2 sessions

### HideShow timer Statistics

John has 12 clients and he wants to use color coding to identify each client. If either a single color or a pair of two different colors can represent a client code, what is the minimum number of colors needed for the coding? Assume that changing the color order within a pair does not produce different codes.

* 24
* 12
* 7
* 6
* 5

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
Senior Manager
Joined: 31 Jul 2008
Posts: 270
Re: Color coding - PS [#permalink]

### Show Tags

26 Aug 2008, 17:39
5 :

let a,b,c,d,e

a ab b c ac bc d ad bd cd e ea ...............
Manager
Joined: 15 Jul 2008
Posts: 205
Re: Color coding - PS [#permalink]

### Show Tags

26 Aug 2008, 18:18
chan4312 wrote:
John has 12 clients and he wants to use color coding to identify each client. If either a single color or a pair of two different colors can represent a client code, what is the minimum number of colors needed for the coding? Assume that changing the color order within a pair does not produce different codes.

* 24
* 12
* 7
* 6
* 5

I think 4 colors would be sufficient
With 2 colors, he can code 2P1 + 2P2 = 4 clients. If a,b are colors then a, b, ab, ba.
With 3 colors 3P1 + 3P2 = 9 clients
With 4 colors 4P1 + 4P2 = 16 clients.

So 4 should be the answer.

If order of color does not matter (which is nonsensical for color code) then 5 colors needed
with 2 colors 2C1 + 2C2 = 2
with 3 colors 3C1 + 3C2 = 6
with 4 colors 4C1 + 4C2 = 10
with 5 colors 5C1 + 5C2 = 15
Intern
Joined: 10 Aug 2008
Posts: 10
Location: Research Triangle Park, NC
Re: Color coding - PS [#permalink]

### Show Tags

26 Aug 2008, 18:32
chan4312 wrote:
John has 12 clients and he wants to use color coding to identify each client. If either a single color or a pair of two different colors can represent a client code, what is the minimum number of colors needed for the coding? Assume that changing the color order within a pair does not produce different codes.

* 24
* 12
* 7
* 6
* 5

You are looking for the number of combinations of one or two colors that sums to at least 12. The giveaway is the "either/or" clause "either a single color or a pair of two" in the stem.

That would be xC1 + xC2 > 12, and x=5 fits the bill.

5C1 + 5C2 > 12 --> 5 + 10 > 12.

cP
_________________

Just a few electrons short of a full cloud...

Manager
Joined: 04 Jun 2008
Posts: 141
Re: Color coding - PS [#permalink]

### Show Tags

26 Aug 2008, 21:38
Thanks buddies
OA is E

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
Re: Color coding - PS   [#permalink] 26 Aug 2008, 21:38
Display posts from previous: Sort by

# John has 12 clients and he wants to use color coding to

Moderators: chetan2u, niks18, Bunuel, KarishmaB

# Events & Promotions

 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®.