Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 16 Jun 2010
Posts: 17

A company that ships boxes to a total of 12 distribution
[#permalink]
Show Tags
Updated on: 31 Jul 2012, 13:49
Question Stats:
64% (01:06) correct 36% (01:12) wrong based on 849 sessions
HideShow timer Statistics
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
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by chintzzz on 16 Jun 2010, 09:23.
Last edited by Bunuel on 31 Jul 2012, 13:49, edited 1 time in total.
Edited the question and added the OA.




Math Expert
Joined: 02 Sep 2009
Posts: 49300

Re: A company that ships boxes to a total of 12 distribution
[#permalink]
Show Tags
19 Dec 2013, 08:10




Manager
Joined: 16 Apr 2010
Posts: 202

Re: need help to solve math question
[#permalink]
Show Tags
16 Jun 2010, 10:12
The answer is 5. 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, Was this my first post ?




Math Expert
Joined: 02 Sep 2009
Posts: 49300

Re: need help to solve math question
[#permalink]
Show Tags
16 Jun 2010, 10:20
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) > \(n+\frac{n(n1)}{2}\geq{12}\) > \(2n+n(n1)\geq{24}\) > \(n(n+1)\geq{24}\) > as \(n\) is an integer (it represents # of colors) \(n\geq{5}\) > \(n_{min}=5\). Answer: B. Hope it's clear.
_________________
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? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 12 Dec 2013
Posts: 3

Re: A company that ships boxes to a total of 12 distribution
[#permalink]
Show Tags
19 Dec 2013, 06:40
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



Manager
Joined: 06 Dec 2014
Posts: 66
Schools: Kelley '18, Owen '18, Moore '18, Boston U '18, Katz '18, Fisher '18, Madison '17, Simon '18, Carroll '18, Smith '18, Broad '18, Terry '18, UrbanaChampaign '18, Rutgers '18, GWU '18, Leeds '18, Northeastern '18, Jenkins FT'18, Weatherhead '18, Carlson PT"18, Fox(Temple)'18

Re: A company that ships boxes to a total of 12 distribution
[#permalink]
Show Tags
18 Feb 2015, 15:23
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/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12425
Location: United States (CA)

Re: A company that ships boxes to a total of 12 distribution
[#permalink]
Show Tags
18 Feb 2015, 22:24
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 1color and 2color codes can you form with the following restrictions: the 2color codes must use 2 DIFFERENT colors and the order of the colors does not matter (so bluegreen is the SAME code as greenblue)? Here, you start with the 5 different 1color codes, then 5c2 different 2color codes = 5 + 10 = 15 codes. GMAT assassins aren't born, they're made, Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/
***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************



Manager
Joined: 06 Dec 2014
Posts: 66
Schools: Kelley '18, Owen '18, Moore '18, Boston U '18, Katz '18, Fisher '18, Madison '17, Simon '18, Carroll '18, Smith '18, Broad '18, Terry '18, UrbanaChampaign '18, Rutgers '18, GWU '18, Leeds '18, Northeastern '18, Jenkins FT'18, Weatherhead '18, Carlson PT"18, Fox(Temple)'18

Re: A company that ships boxes to a total of 12 distribution
[#permalink]
Show Tags
19 Feb 2015, 13:59
Thanks for the reply 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/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12425
Location: United States (CA)

Re: A company that ships boxes to a total of 12 distribution
[#permalink]
Show Tags
19 Feb 2015, 14:24
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
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/
***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************



Manager
Joined: 28 Apr 2016
Posts: 97

Re: A company that ships boxes to a total of 12 distribution
[#permalink]
Show Tags
12 Jul 2016, 21:14
I am confused with the line 'order doesn't matter'. Does it mean BR = RB or BR =/ to RB?. ij78cp wrote: 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



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12425
Location: United States (CA)

Re: A company that ships boxes to a total of 12 distribution
[#permalink]
Show Tags
14 Jul 2016, 07:06
Hi ameyaprabhu, When the order doesn't matter, RB and BR are the SAME option (so you can't count it twice, you can only count it once). In these sorts of questions, it can often be fastest to just 'list out' the possibilities (as opposed to doing lots of complex calculations). GMAT assassins aren't born, they're made, Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/
***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************



Intern
Joined: 27 Oct 2016
Posts: 3
Location: Argentina
Concentration: General Management, Operations
WE: Engineering (Energy and Utilities)

Re: A company that ships boxes to a total of 12 distribution
[#permalink]
Show Tags
22 Feb 2017, 02:41
Hi writing the possibilities should be like this: 1color code: A, B, C, D, E > 5 POS. 2color code: AB, AC, BC, DA, DB, DC, EA, EB, EC, ED > 10 POS. ij78cp wrote: 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



Intern
Joined: 07 Apr 2017
Posts: 5

Re: A company that ships boxes to a total of 12 distribution
[#permalink]
Show Tags
24 Apr 2017, 23:50
Bunuel wrote: 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) > \(n+\frac{n(n1)}{2}\geq{12}\) > \(2n+n(n1)\geq{24}\) > \(n(n+1)\geq{24}\) > as \(n\) is an integer (it represents # of colors) \(n\geq{5}\) > \(n_{min}=5\). Answer: B. Hope it's clear. Could you please explain me how you get [fraction]n(n1)/2 from C^2_n? Shouldn't it be [fraction]n!/k!(nk)! ? Thanks



Math Expert
Joined: 02 Sep 2009
Posts: 49300

Re: A company that ships boxes to a total of 12 distribution
[#permalink]
Show Tags
25 Apr 2017, 02:04
matteogr wrote: Bunuel wrote: 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) > \(n+\frac{n(n1)}{2}\geq{12}\) > \(2n+n(n1)\geq{24}\) > \(n(n+1)\geq{24}\) > as \(n\) is an integer (it represents # of colors) \(n\geq{5}\) > \(n_{min}=5\). Answer: B. Hope it's clear. Could you please explain me how you get n(n1)/2 from C^2_n? Shouldn't it be n!/k!(nk)! ? Thanks \(C^2_n=\frac{n!}{(n2)!*2!}=\frac{(n2)!*(n1)*n}{(n2)!*2!}=\frac{(n1)*n}{2}\). Hope it's clear.
_________________
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? Extrahard Quant Tests with Brilliant Analytics



Director
Joined: 17 Dec 2012
Posts: 636
Location: India

Re: A company that ships boxes to a total of 12 distribution
[#permalink]
Show Tags
20 May 2017, 20:13
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 1. Solving a simple case and then generalizing would be easy for this problem. 2. Take 2 colors Red and Blue. These two can be used in the following ways R, B, RB. i.e, 2+2C2. It can represent only 3 centers 3. Take 3 colors R, B, G. These can represent 3 +3c2=6 centers 4. Four colors can represent 4+4C2= 10 centers 5 colors can represent 5+5C2=15 centers So we see a minimum of 5 colors are needed
_________________
Srinivasan Vaidyaraman Sravna Holistic Solutions http://www.sravnatestprep.com
Holistic and Systematic Approach



Senior Manager
Joined: 24 Oct 2016
Posts: 285
Location: India
Concentration: Finance, International Business
GPA: 3.96
WE: Human Resources (Retail Banking)

Re: A company that ships boxes to a total of 12 distribution
[#permalink]
Show Tags
21 May 2017, 08:44
the answer is 5 see if we have 4 different colors then we have 4 unique single identity and 4*3/1*2=6 unique identity with pairs so slightly more than 4 will be the answer that is 5



Manager
Joined: 23 Dec 2013
Posts: 181
Location: United States (CA)
GMAT 1: 710 Q45 V41 GMAT 2: 760 Q49 V44
GPA: 3.76

Re: A company that ships boxes to a total of 12 distribution
[#permalink]
Show Tags
02 Jun 2017, 11:11
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 For this problem, you can simply list out the possibilities. Since it's a min/max problem, starting with A is best. Repetition of colors is not allowed. A) n = 4 Let ABCD represent four colors. ABCD = 4 centers covered AB AC AD = 3 more centers BC BD = 2 more centers CD = 1 more center The total here is 11. Since we are close to 12, an increase in one color should be more than enough. B is the answer.



Intern
Joined: 27 Nov 2016
Posts: 5

Re: A company that ships boxes to a total of 12 distribution
[#permalink]
Show Tags
02 Jun 2017, 12:11
Solve this using algebra
nC2 + nC1 >= 12
n*(n1)/2 + n >= 12
Testing the answer options , 5 is the minimum value which satisfies the condition.
Sent from my iPhone using GMAT Club Forum



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2835

Re: A company that ships boxes to a total of 12 distribution
[#permalink]
Show Tags
08 Mar 2018, 17:48
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 Since we have only 12 distribution centers, we know we will need fewer than 12 different colors to identify them. Let’s say we have 4 different colors; then 4C1 = 4 centers can be identified by one color, and 4C2 = 6 centers can be identified by two different colors. So a total of 4 + 6 = 10 centers can be identified. We see that if we have only 4 different colors, we don’t have enough ID codes to assign to the 12 centers. Therefore, we need one more color. If we have 5 different colors, then 5C1 = 5 centers can be identified by one color, and 5C2 = 10 centers can be identified by two different colors. So a total of 5 + 10 = 15 centers can be identified. We see that if we have 5 different colors, we have more than enough ID codes to assign to the 12 centers. Answer: B
_________________
Jeffery Miller
Head of GMAT Instruction
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions




Re: A company that ships boxes to a total of 12 distribution &nbs
[#permalink]
08 Mar 2018, 17:48






