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

 It is currently 22 Feb 2019, 08:32

### 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 February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
• ### Free GMAT RC Webinar

February 23, 2019

February 23, 2019

07:00 AM PST

09:00 AM PST

Learn reading strategies that can help even non-voracious reader to master GMAT RC. Saturday, February 23rd at 7 AM PT
• ### FREE Quant Workshop by e-GMAT!

February 24, 2019

February 24, 2019

07:00 AM PST

09:00 AM PST

Get personalized insights on how to achieve your Target Quant Score.

# In a certain city each of 20 Girl Scout troops is represente

Author Message
TAGS:

### Hide Tags

Intern
Joined: 15 Aug 2010
Posts: 8
Concentration: Healthcare, Marketing
WE: Other (Health Care)
In a certain city each of 20 Girl Scout troops is represente  [#permalink]

### Show Tags

Updated on: 23 May 2014, 11:53
13
00:00

Difficulty:

45% (medium)

Question Stats:

65% (01:52) correct 35% (01:43) wrong based on 224 sessions

### HideShow timer Statistics

In a certain city each of 20 Girl Scout troops is represented by a colored flag. Each flag consists of either a single color or a pair of two different colors. If each troop has a different flag, what is the minimum number of colors needed for the flags. (Assume that the order of colors in a pair on a flag does not matter.)

A. 5
B. 6
C. 10
D. 20
E. 40

Originally posted by GMATSept on 28 Aug 2010, 21:36.
Last edited by Bunuel on 23 May 2014, 11:53, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
Manager
Joined: 09 Jun 2010
Posts: 101

### Show Tags

28 Aug 2010, 22:50
Hi GMATSept,

The question is basically asking us to find a number N such that N+ NC2 >20 (since there are 20 different groups)
Its best to back solve. Will save a lot of time.

if N= 5 => N+NC2 = 5 + 5C2 = 5+10 = 15

If N = 6 => N+ NC2 = 6 + 6C2 = 6+15 = 21

as 21 > 20 therefore 6 different colors will be sufficient to give more than 20 different flags.

Director
Status: Everyone is a leader. Just stop listening to others.
Joined: 22 Mar 2013
Posts: 768
Location: India
GPA: 3.51
WE: Information Technology (Computer Software)

### Show Tags

23 May 2014, 11:47
B.6:
if we have 6 colors we can choose pairs in 6C2 ways = 15 and single color flags are 6. Therefore total number of flags = 21.
ANS B.
_________________

Piyush K
-----------------------
Our greatest weakness lies in giving up. The most certain way to succeed is to try just one more time. ― Thomas A. Edison
Don't forget to press--> Kudos
My Articles: 1. WOULD: when to use? | 2. All GMATPrep RCs (New)
Tip: Before exam a week earlier don't forget to exhaust all gmatprep problems specially for "sentence correction".

Math Expert
Joined: 02 Sep 2009
Posts: 53067
Re: In a certain city each of 20 Girl Scout troops is represente  [#permalink]

### Show Tags

23 May 2014, 11:59
GMATSept wrote:
In a certain city each of 20 Girl Scout troops is represented by a colored flag. Each flag consists of either a single color or a pair of two different colors. If each troop has a different flag, what is the minimum number of colors needed for the flags. (Assume that the order of colors in a pair on a flag does not matter.)

A. 5
B. 6
C. 10
D. 20
E. 40

Combination approach:

Let the # of colors needed is $$n$$, then it must be true that $$n+C^2_n\geq{20}$$ ($$C^2_n$$ - # of ways to choose the pair of different colors from $$n$$ colors when order doesn't matter) --> $$n+\frac{n(n-1)}{2}\geq{20}$$ --> $$2n+n(n-1)\geq{40}$$ --> $$n(n+1)\geq{40}$$ --> as $$n$$ is an integer (it represents # of colors) $$n\geq{6}$$ --> $$n_{min}=6$$.

Trial and error approach:

If the minimum number of colors needed is 5 then there are 5 single color flags possible PLUS $$C^2_5=10$$ two-color flags --> 5+10=15<20 --> not enough for 12 codes;

If the minimum number of colors needed is 6 then there are 6 single color flags possible PLUS $$C^2_6=15$$ two-color codes --> 6+15=21>20 --> more than enough for 20 flags.

Similar questions to practice:

each-student-at-a-certain-university-is-given-a-four-charact-151945.html
all-of-the-stocks-on-the-over-the-counter-market-are-126630.html
if-a-code-word-is-defined-to-be-a-sequence-of-different-126652.html
a-4-letter-code-word-consists-of-letters-a-b-and-c-if-the-59065.html
a-5-digit-code-consists-of-one-number-digit-chosen-from-132263.html
a-company-that-ships-boxes-to-a-total-of-12-distribution-95946.html
a-company-plans-to-assign-identification-numbers-to-its-empl-69248.html
the-security-gate-at-a-storage-facility-requires-a-five-109932.html
all-of-the-bonds-on-a-certain-exchange-are-designated-by-a-150820.html
a-local-bank-that-has-15-branches-uses-a-two-digit-code-to-98109.html
a-researcher-plans-to-identify-each-participant-in-a-certain-134584.html
baker-s-dozen-128782-20.html#p1057502
in-a-certain-appliance-store-each-model-of-television-is-136646.html
m04q29-color-coding-70074.html
john-has-12-clients-and-he-wants-to-use-color-coding-to-iden-107307.html
how-many-4-digit-even-numbers-do-not-use-any-digit-more-than-101874.html
a-certain-stock-exchange-designates-each-stock-with-a-85831.html
the-simplastic-language-has-only-2-unique-values-and-105845.html
m04q29-color-coding-70074.html
a-researcher-plans-to-identify-each-participant-in-a-certain-134584-20.html

Hope this helps.
_________________
Manager
Joined: 11 Nov 2011
Posts: 62
Location: United States
Concentration: Finance, Human Resources
GPA: 3.33
WE: Consulting (Non-Profit and Government)
Re: In a certain city each of 20 Girl Scout troops is represente  [#permalink]

### Show Tags

27 Apr 2015, 06:00
Can you explain this part, please? $$C^2_n$$ --> $$\frac{n(n-1)}{2}$$
Math Expert
Joined: 02 Sep 2009
Posts: 53067
Re: In a certain city each of 20 Girl Scout troops is represente  [#permalink]

### Show Tags

27 Apr 2015, 06:08
evdo wrote:
Can you explain this part, please? $$C^2_n$$ --> $$\frac{n(n-1)}{2}$$

$$C^2_n=\frac{n!}{2!*(n-2)!}=\frac{(n-2)!*(n-1)*n}{2!*(n-2)!}=\frac{(n-1)*n}{2}$$
_________________
Manager
Joined: 11 Nov 2011
Posts: 62
Location: United States
Concentration: Finance, Human Resources
GPA: 3.33
WE: Consulting (Non-Profit and Government)
Re: In a certain city each of 20 Girl Scout troops is represente  [#permalink]

### Show Tags

27 Apr 2015, 07:00
thanks a lot Bunuel... completely forgot the formula of combination
Manager
Joined: 20 Apr 2013
Posts: 126
Re: In a certain city each of 20 Girl Scout troops is represente  [#permalink]

### Show Tags

27 Apr 2015, 10:54
We have to find the minimum value of the number of colors (n) such that when they are used as 1 color flags or 2 color flags, they are able to represent at least 20 different combinations.

So, C(n,1) + C(n,2) >= 20
n + n(n-1)/2 >= 20
n^2 + n >= 40

So, the minimum value of n that satisfies this is n=6.
Manager
Joined: 26 May 2013
Posts: 94
Re: In a certain city each of 20 Girl Scout troops is represente  [#permalink]

### Show Tags

28 Apr 2015, 05:25
I would say combinatorics is the wrong way to approach this problem, unless you can see that right away you will be plugging in the answer choices.

My approach:

Color 1= 1 total
Color 2: Color1/2 = 2 total
Color 3: Color1/3, Color 2/3 = 3 total
Color 4: Color1/4, Color 2/4, Color 3/4 = 4 total
Color 5: Color1/5, Color2/5, Color3/5, Color 4/5 = 5 total
Color 6: ........ 6 total.

Therefore the min number of colors needed is 6.
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 4955
Location: United States (CA)
Re: In a certain city each of 20 Girl Scout troops is represente  [#permalink]

### Show Tags

15 Mar 2017, 15:32
GMATSept wrote:
In a certain city each of 20 Girl Scout troops is represented by a colored flag. Each flag consists of either a single color or a pair of two different colors. If each troop has a different flag, what is the minimum number of colors needed for the flags. (Assume that the order of colors in a pair on a flag does not matter.)

A. 5
B. 6
C. 10
D. 20
E. 40

We can denote our colors with a letter of the alphabet.

A

B, AB

C, AC, BC

E, AE, BE, CE, DE

F, AF, BF, CF, DF, EF (we see that we could have stopped at DF, since that was the 20th flag.)

Thus, we see that 6 colors are needed.

Alternate Solution:

Let’s say we need at least n colors to satisfy the requirement. Let’s calculate the number of different flags that can be represented using n colors: The number of single-color flags is n and the number of two-color flags is nC2 = n(n - 1)/2. Therefore, we need:

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

2n + n^2 - n > 40

n^2 + n > 40

Looking at the answer choices, we see that n = 6 is the smallest value that satisfies this inequality.

_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Non-Human User
Joined: 09 Sep 2013
Posts: 9894
Re: In a certain city each of 20 Girl Scout troops is represente  [#permalink]

### Show Tags

16 Oct 2018, 06:12
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.
_________________
Re: In a certain city each of 20 Girl Scout troops is represente   [#permalink] 16 Oct 2018, 06:12
Display posts from previous: Sort by