NEW HERE? LEARN MORE
closeclose
Last visit was: 26 Apr 2024, 07:42 It is currently 26 Apr 2024, 07:42
Decision Tracker
My Rewards
New posts
New comers' posts

Close
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
Your Progress

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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

In a certain laboratory, chemicals are identified by a color-coding sy

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92935
Own Kudos [?]: 619177 [18]
Given Kudos: 81609
Send PM
CAT Tests Forum Quiz Mode
In a certain laboratory, chemicals are identified by a color-coding sy [#permalink] New post   12 Dec 2018, 03:24
18
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

45% (medium)

Question Stats:

62% (01:42) correct 38% (01:48) wrong based on 250 sessions
Hide Show timer Statistics
In a certain laboratory, chemicals are identified by a color-coding system. There are 20 different chemicals. Each one is coded with either a single color or a unique two-color pair. If the order of colors in the pairs doesn't matter, what is the minimum number of different colors needed to code all 20 chemicals with either a single color or a unique pair of colors?

A. 5
B. 6
C. 7
D. 20
E. 40
ShowHide Answer
Official Answer
B
Most Helpful Reply
User avatar
L
ScottTargetTestPrep
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 18761
Own Kudos [?]: 22056 [7]
Given Kudos: 283
Location: United States (CA)
Send PM
Re: In a certain laboratory, chemicals are identified by a color-coding sy [#permalink] New post   06 Jun 2019, 18:01
4
Kudos
3
Bookmarks
Expert Reply
Bunuel wrote:
In a certain laboratory, chemicals are identified by a color-coding system. There are 20 different chemicals. Each one is coded with either a single color or a unique two-color pair. If the order of colors in the pairs doesn't matter, what is the minimum number of different colors needed to code all 20 chemicals with either a single color or a unique pair of colors?

A. 5
B. 6
C. 7
D. 20
E. 40


Let’s analyze the answer choices.

If there are 5 different colors, the number of codes that can be formed is 5C1 + 5C2 = 5 + 10 = 15, which is not sufficient for the 20 different chemicals.

If there are 6 different colors, the number of codes that can be formed is 6C1 + 6C2 = 6 + 15 = 21, which IS sufficient for the 20 different chemicals. Therefore, we need at least 6 different colors.

Answer: B
User avatar
G
RJ7X0DefiningMyX
Manager
Manager
Joined: 08 Apr 2019
Posts: 102
Own Kudos [?]: 306 [0]
Given Kudos: 259
Location: India
GPA: 4
Send PM
Re: In a certain laboratory, chemicals are identified by a color-coding sy [#permalink] New post   05 Jun 2019, 05:14
Bunuel wrote:
In a certain laboratory, chemicals are identified by a color-coding system. There are 20 different chemicals. Each one is coded with either a single color or a unique two-color pair. If the order of colors in the pairs doesn't matter, what is the minimum number of different colors needed to code all 20 chemicals with either a single color or a unique pair of colors?

A. 5
B. 6
C. 7
D. 20
E. 40


Shouldn't the approach to solve this question be the following:

Let the number of colours be 'n', and we have n + n(n-1)/2 >= 20

We get 2n + n^2 - n = 40, simplifying further we get n^2 + n = 40

Now, putting in the values (since we only require the minimum no. of colors), we see that n cannot be equal to 5 and 6 is the first (and the minimum) value that satisfies the equation.

Hence, option (B)
General Discussion
User avatar
L
Archit3110
GMAT Club Legend
GMAT Club Legend
Joined: 18 Aug 2017
Status:You learn more from failure than from success.
Posts: 8020
Own Kudos [?]: 4098 [0]
Given Kudos: 242
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1:
545 Q79 V79 DI73
GPA: 4
WE:Marketing (Energy and Utilities)
Send PM
GMAT ToolKit User CAT Tests
In a certain laboratory, chemicals are identified by a color-coding sy [#permalink] New post   12 Dec 2018, 03:33
Bunuel wrote:
In a certain laboratory, chemicals are identified by a color-coding system. There are 20 different chemicals. Each one is coded with either a single color or a unique two-color pair. If the order of colors in the pairs doesn't matter, what is the minimum number of different colors needed to code all 20 chemicals with either a single color or a unique pair of colors?

A. 5
B. 6
C. 7
D. 20
E. 40



6c1 +6c2 : 21

IMO 6 should be correct.. IMO b
User avatar
G
pandeyashwin
Manager
Manager
Joined: 14 Jun 2018
Posts: 171
Own Kudos [?]: 257 [1]
Given Kudos: 176
Send PM
Re: In a certain laboratory, chemicals are identified by a color-coding sy [#permalink] New post   12 Dec 2018, 10:07
1
Bookmarks
Let say there are 2 colors : A & B. All possible combination would be A , B , AB.
If there are 3 : A, B & C. Combinations would be A , B , C , AB, AC , BC.

n(n+1)/ 2 > 20
n(n+1) > 40

Lowest value which fits is 6.

Ans B
User avatar
S
kanakdaga
Manager
Manager
Joined: 12 Dec 2017
Posts: 66
Own Kudos [?]: 153 [0]
Given Kudos: 52
Location: India
Schools: XLRI GMBA '20 Yale '19
GMAT 1: 660 Q46 V35
GPA: 3.8
Send PM
In a certain laboratory, chemicals are identified by a color-coding sy [#permalink] New post   04 Jan 2019, 03:19
In a certain laboratory, chemicals are identified by a color-coding system. There are 20 different chemicals. Each one is coded with either a single color or a unique two-color pair. If the order of colors in the pairs doesn't matter, what is the minimum number of different colors needed to code all 20 chemicals with either a single color or a unique pair of colors?

CONSIDER ANSWER CHOICES

5 colours

A,B,C,D,E
AB, AC, AD, AE
BC, BD, BE
CD, CE
DE
falls short of 20.

6 colours

all the above + a new colour F
F, FA, FB, FC,FD, FE
totals 21.

B is the correct option.
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32685
Own Kudos [?]: 822 [0]
Given Kudos: 0
Send PM
Re: In a certain laboratory, chemicals are identified by a color-coding sy [#permalink] New post   29 Dec 2022, 03:52
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.
GMAT Club Bot
gmatclubot
Re: In a certain laboratory, chemicals are identified by a color-coding sy [#permalink]
29 Dec 2022, 03:52
Moderators:
Bunuel
Math Expert
92933 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions