Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 06 May 2015, 21:00

### 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

# A company that ships boxes to a total of 12 distribution

Author Message
TAGS:
Intern
Joined: 16 Jun 2010
Posts: 22
Followers: 0

Kudos [?]: 17 [0], given: 0

A company that ships boxes to a total of 12 distribution [#permalink]  16 Jun 2010, 08:23
6
This post was
BOOKMARKED
00:00

Difficulty:

35% (medium)

Question Stats:

66% (02:05) correct 34% (01:06) wrong based on 289 sessions
A company that ships boxes to a total of 12 distribution centers uses color coding to identify each center. If either a single color or a pair of two different colors is chosen to represent each center and if each center is uniquely represented by that choice of one or two colors, what is the minimum number of colors needed for the coding? (assume that the order of colors in a pair does not matter)

A. 4
B. 5
C. 6
D. 12
E. 24
[Reveal] Spoiler: OA

Last edited by Bunuel on 31 Jul 2012, 12:49, edited 1 time in total.
Edited the question and added the OA.
Manager
Joined: 16 Apr 2010
Posts: 222
Followers: 3

Kudos [?]: 63 [1] , given: 12

Re: need help to solve math question [#permalink]  16 Jun 2010, 09:12
1
KUDOS
1
This post was
BOOKMARKED

This is a combination problem that can be formulated in the following matter:
XC1 + XC2 >= 12

Lets try answer 4. We will get 4C1+4C2= 4+6 which is less than 10.
Trying 5, we will get 5C1+5C2= 5+10 which is greater than 12,

Math Expert
Joined: 02 Sep 2009
Posts: 27238
Followers: 4237

Kudos [?]: 41166 [1] , given: 5672

Re: need help to solve math question [#permalink]  16 Jun 2010, 09:20
1
KUDOS
Expert's post
chintzzz wrote:
A company that ships boxes to a total of 12 distribution centers uses color coding to identify each center. If either a single color or a pair of two different colors is chosen to represent each center and if each center is uniquely represented by that choice of one or two colors, what is the minimum number of colors needed for the coding? (assume that the order of colors in a pair does not matter)
A)4
B)5
C)6
D)12
E)24

You can solve by trial and error or use algebra.

Let # of colors needed be $$n$$, then it must be true that $$n+C^2_n\geq{12}$$ ($$C^2_n$$ - # of ways to choose the pair of different colors from $$n$$ colors when order doesn't matter) --> $$n+\frac{n(n-1)}{2}\geq{12}$$ --> $$2n+n(n-1)\geq{24}$$ --> $$n(n+1)\geq{24}$$ --> as $$n$$ is an integer (it represents # of colors) $$n\geq{5}$$ --> $$n_{min}=5$$.

Hope it's clear.
_________________
Director
Status: No dream is too large, no dreamer is too small
Joined: 14 Jul 2010
Posts: 663
Followers: 36

Kudos [?]: 355 [0], given: 39

Combination QR [#permalink]  18 Feb 2011, 07:22
A company that ships boxes to a total of 12 distribution centers uses color coding to identify each center. If either a single color or a pair of two different colors is chosen to represent each center and if each center is uniquely represented by that choice of one or two colors, what is the minimum number of colors needed for the coding? (Assume that the order of the colors in a pair does not matter.)
(A) 4
(B) 5
(C) 6
(D) 12
(E) 24
_________________

Collections:-
PSof OG solved by GC members: http://gmatclub.com/forum/collection-ps-with-solution-from-gmatclub-110005.html
DS of OG solved by GC members: http://gmatclub.com/forum/collection-ds-with-solution-from-gmatclub-110004.html
100 GMAT PREP Quantitative collection http://gmatclub.com/forum/gmat-prep-problem-collections-114358.html
Collections of work/rate problems with solutions http://gmatclub.com/forum/collections-of-work-rate-problem-with-solutions-118919.html
Mixture problems in a file with best solutions: http://gmatclub.com/forum/mixture-problems-with-best-and-easy-solutions-all-together-124644.html

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 4791
Followers: 296

Kudos [?]: 52 [0], given: 0

Re: A company that ships boxes to a total of 12 distribution [#permalink]  27 Sep 2013, 04:04
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: 12 Dec 2013
Posts: 3
Followers: 0

Kudos [?]: 0 [0], given: 9

Re: A company that ships boxes to a total of 12 distribution [#permalink]  19 Dec 2013, 05:40
I tried to do it with writing the possibilities out:

B(Blue) R(Red) Y(Yellow) P(Pink)

B
BR
RB
R
Y
YR
YB
RY
BY
P
PR
RP
PB
BP
PY
YP

I already reach 16 different combinations with only 4 colours, but the OA is 5? what´s my mistake?

EDIT:

Just figured that the ordering does not count as 2 different orders.. therefore, we need 5 colours.. thanks anyway
Math Expert
Joined: 02 Sep 2009
Posts: 27238
Followers: 4237

Kudos [?]: 41166 [0], given: 5672

Re: A company that ships boxes to a total of 12 distribution [#permalink]  19 Dec 2013, 07:10
Expert's post
3
This post was
BOOKMARKED
Intern
Joined: 06 Dec 2014
Posts: 43
Followers: 0

Kudos [?]: 0 [0], given: 4

Re: A company that ships boxes to a total of 12 distribution [#permalink]  18 Feb 2015, 14:23
Can anyone tell me when we use n^2 and when we use n+nC2 ????

In this color question we use n+nC2 >= 12

In integer questions we use n^2>=15 ....
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 1908
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Followers: 79

Kudos [?]: 502 [0], given: 38

Re: A company that ships boxes to a total of 12 distribution [#permalink]  18 Feb 2015, 21:24
Expert's post
Hi gmathopeful90,

The "restrictions" in the question are what dictate the math.

Consider these possible scenarios:

1) You have 5 different colors to choose from and two different rooms to paint. You can use the same color in both rooms. How many different color combinations are there for the two rooms?

Here, the first room could be 5 different colors and the second room could be 5 different colors, so (5)(5) = 5^2 = 25 options.

2) You have 5 different colors to choose from and two different rooms to paint. You CANNOT use the same color in both rooms. How many different color combinations are there for the two rooms?

Here, the first room could be 5 different colors; once you assign that first color, the second room could only be 4 different colors, so (5)(4) = 20 options.

3) You have 5 different colors to choose from. How many different 1-color and 2-color codes can you form with the following restrictions: the 2-color codes must use 2 DIFFERENT colors and the order of the colors does not matter (so blue-green is the SAME code as green-blue)?

Here, you start with the 5 different 1-color codes, then 5c2 different 2-color codes = 5 + 10 = 15 codes.

GMAT assassins aren't born, they're made,
Rich
_________________

Rich Cohen
Rich.C@empowergmat.com
http://www.empowergmat.com

EMPOWERgmat GMAT Club Page, Study Plans, & Discounts

Intern
Joined: 06 Dec 2014
Posts: 43
Followers: 0

Kudos [?]: 0 [0], given: 4

Re: A company that ships boxes to a total of 12 distribution [#permalink]  19 Feb 2015, 12:59

Do you mean in questions where we assume order of colors in cominations matters, we can use 5*4..
But where color doesn't matter, we use 5C2 ???

This explains stuff for me
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 1908
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Followers: 79

Kudos [?]: 502 [0], given: 38

Re: A company that ships boxes to a total of 12 distribution [#permalink]  19 Feb 2015, 13:24
Expert's post
Hi gmathopeful90,

You've hit on THE key difference between Permutation and Combination questions: does the order MATTER or not.

IF you're putting things in order (the word "arrange" or "arrangements" often shows up in these types of questions), then you have to keep track of the number of options at each "step" and standard multiplication is involved.

IF you're picking combinations of things (the word "combination" is the common word in these questions), then the order of the items does NOT matter and you have to use the Combination Formula.

One of the interesting "design elements" of Official GMAT questions is that you can use either of the above approaches on certain types of prompts - you just have to be careful about how you set up the math (and you have to be really organized with your work).

GMAT assassins aren't born, they're made,
Rich
_________________

Rich Cohen
Rich.C@empowergmat.com
http://www.empowergmat.com

EMPOWERgmat GMAT Club Page, Study Plans, & Discounts

Re: A company that ships boxes to a total of 12 distribution   [#permalink] 19 Feb 2015, 13:24
Similar topics Replies Last post
Similar
Topics:
13 A company that ships boxes to a total of 12 distribution cen 7 06 Mar 2014, 01:57
A company that ships boxes to a total of 12 distribution 3 04 Oct 2011, 19:37
A company that ships boxes to a total of 12 distribution 3 16 Oct 2008, 12:45
A company that ships boxes to a total of 12 distribution 2 01 Oct 2007, 03:01
A company that ships boxes to a total of 12 distribution 7 09 Sep 2005, 19:44
Display posts from previous: Sort by