OG #132

Expert replies

jc114: Senior | Next Rank: 100 Posts; Posts: 53; Joined: Thu Apr 12, 2007 12:32 am; Thanked: 1 times

by jc114 » Fri Apr 13, 2007 7:42 am

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 2 colors, what is the minimum # 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

Like this post

Source: Beat The GMAT — Problem Solving | Fri Apr 13, 2007 7:42 am

jaspetrovic: Junior | Next Rank: 30 Posts; Posts: 26; Joined: Fri Mar 16, 2007 1:32 pm

by jaspetrovic » Fri Apr 13, 2007 8:15 am

Hi there

Tere are 2 ways to solve this question.

As I first saw this q. I knew that it tests the use of combinations, but I used a little bit different app. Itlooked faster to me.
I looked at the ansers and started to backsolve. I marked colors w/numbers: 1, 2, 3, 4,...
So, in A - we have 4 combinations w/one color and 6 combinations w/2 colors(12, 13, 14, 23, 24, 34) => 4 + 6=10<12 NOT enough

B - 5 comb. w/ one color and 10 comb. w/2 colors (12, 13, 14, 15, 23, 24, 25, 34, 35, 45) => 5+10=15>12 MORE than enough

Later I saw the 2nd app. through use of combination formula.
Ok, so in A we have 4 colors so we need 8 comb. of two colors (12-4). 4!/2!(4-2)!=6<8. We need more colors. If we use 5 color we would need (12-5) 7 comb. of 2 colors => 5!/2!(5-2)!=10>7

So, B is the answer

Like this post

Cybermusings: Legendary Member; Posts: 559; Joined: Tue Mar 27, 2007 1:29 amFollowed by: 2 members; Thanked: 5 times

by Cybermusings » Sat Apr 14, 2007 2:58 am

Is the answer 5?

Like this post

GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8199; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Mon May 20, 2019 6:08 pm

jc114 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 2 colors, what is the minimum # 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

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

Scott Woodbury-Stewart
Founder and CEO
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

Like this post

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Tue May 21, 2019 6:31 am

jc114 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 2 colors, what is the minimum # 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

We need to be able to create AT LEAST 12 codes (to represent the 12 countries).

Let's test the options.
Can we get 12 or more color codes with 4 colors?
Let's see . . .

1-color codes = 4 (since there are 4 colors)
2-color codes = We need to choose 2 colors from 4. This can be accomplished in 4C2 ways (using combinations). 4C2 = 6
So, using 4 colors, the total number of color codes we can create = 4 + 6 = 10
We want to create AT LEAST 12 color codes, so we can eliminate answer choice A.

Aside: If anyone is interested, here's a video on calculating combinations (like 4C2) in your head: https://www.gmatprepnow.com/module/gmat-counting?id=789

Can we get 12 or more color codes with 5 colors?
1-color codes = 5 (since there are 5 colors)
2-color codes = We need to choose 2 colors from 5. This can be accomplished in 5C2 ways (using combinations). 5C2 = 10
So, using 5 colors, the total number of color codes we can create = 5 + 10 = 15
Perfect!

The answer is 5 (B)

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review