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

It is currently 20 Feb 2019, 20:00

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.

Close

Request Expert Reply

Confirm Cancel
Events & Promotions in February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
  • Free GMAT Prep Hour

     February 20, 2019

     February 20, 2019

     08:00 PM EST

     09:00 PM EST

    Strategies and techniques for approaching featured GMAT topics. Wednesday, February 20th at 8 PM EST
  • Online GMAT boot camp for FREE

     February 21, 2019

     February 21, 2019

     10:00 PM PST

     11:00 PM PST

    Kick off your 2019 GMAT prep with a free 7-day boot camp that includes free online lessons, webinars, and a full GMAT course access. Limited for the first 99 registrants! Feb. 21st until the 27th.

In how many different ways can 3 boys and 3 girls be seated in a row

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

 
Intern
Intern
avatar
Joined: 08 Jan 2015
Posts: 25
In how many different ways can 3 girls and 3 boys be seated at a recta  [#permalink]

Show Tags

New post 30 Mar 2015, 10:35
2
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

69% (00:54) correct 31% (00:58) wrong based on 160 sessions

HideShow timer Statistics

In how many different ways can 3 girls and 3 boys be seated at a rectangular table that has 3 chairs on one side and 3 stools on the other side, if two girls or two boys can never sit side by side?

A. 24
B. 36
C. 72
D. 84
E. 96
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 13562
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: In how many different ways can 3 girls and 3 boys be seated at a recta  [#permalink]

Show Tags

New post 30 Mar 2015, 11:59
1
Hi Awli,

The prompt gives us the specific restriction that a boy can't sit next to another boy and a girl can't sit next to another girl. Since there are chairs on one side of the table and stools on the other side of the table, we have to account for 2 possible seating arrangements:

BGB
GBG

and

GBG
BGB

From here, we can use a simple permutation to get to the answer:

Moving from left-to-right....
For the first "spot", there are 3 different boys to choose from
For the second "spot", there are 3 different girls to choose from
For the third "spot", there then 2 different boys to choose from
For the fourth "spot", there are then 2 different girls to choose form
For the fifth and sixth "spots", we have the 1 boy and 1 girl that are left

(3)(3)(2)(2)(1)(1) = 36 possible seating arrangements for each of the two options.

(36)(2) = 72

Final Answer:

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

Co-Founder & 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!*****

Veritas Prep GMAT Instructor
User avatar
D
Joined: 16 Oct 2010
Posts: 8888
Location: Pune, India
Re: In how many different ways can 3 girls and 3 boys be seated at a recta  [#permalink]

Show Tags

New post 30 Mar 2015, 23:21
1
Awli wrote:
In how many different ways can 3 girls and 3 boys be seated at a rectangular table that has 3 chairs on one side and 3 stools on the other side, if two girls or two boys can never sit side by side?

A. 24
B. 36
C. 72
D. 84
E. 96


Since 3 people will be on each side, and no two boys/two girls can sit together, on one side you will have Boy-Girl-Boy arrangement and on the other side you will have Girl-Boy-Girl arrangement.
From the 3 boys, choose 2 in 3C2 ways and a girl in 3C1 ways. Now you have split the boys and girls into BGB and GBG.
For BGB, pick a side (either chairs or stools) in 2 ways.
The girl takes the center seat and the 2 boys can be arranged around the girl in 2! ways.
On the other side, the boy sits in the center and the girls are arranged on his two sides in 2! ways.

Total arrangements = 3C2 * 3C1 * 2 * 2! * 2! = 72 ways.

Answer (C)
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

Manager
Manager
avatar
Joined: 13 Apr 2016
Posts: 59
Location: India
GMAT 1: 640 Q50 V27
GPA: 3
WE: Operations (Hospitality and Tourism)
Re: In how many different ways can 3 girls and 3 boys be seated at a recta  [#permalink]

Show Tags

New post 07 May 2016, 07:51
3
Awli wrote:
In how many different ways can 3 girls and 3 boys be seated at a rectangular table that has 3 chairs on one side and 3 stools on the other side, if two girls or two boys can never sit side by side?

A. 24
B. 36
C. 72
D. 84
E. 96


ans C
Figure attached
Attachments

1.jpg
1.jpg [ 304.35 KiB | Viewed 3037 times ]

Senior Manager
Senior Manager
avatar
B
Joined: 13 Oct 2016
Posts: 367
GPA: 3.98
Re: In how many different ways can 3 boys and 3 girls be seated in a row  [#permalink]

Show Tags

New post 04 Jan 2017, 00:12
1
3!*3!*2! = 6*6*2 = 72

Answer C
CEO
CEO
User avatar
P
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2788
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Reviews Badge
Re: In how many different ways can 3 boys and 3 girls be seated in a row  [#permalink]

Show Tags

New post 04 Jan 2017, 01:32
3
Bunuel wrote:
In how many different ways can 3 boys and 3 girls be seated in a row of 6 chairs such that the girls are not separated, and the boys are not separated?

A. 24
B. 36
C. 72
D. 144
E. 288


Lets consider the group of all boys as one entity and group of girls as other entity

Now we have two entities to arrange which is possible in 2! ways

The group of boys within itself can be rearranged in 3! ways and
The group of Girls within itself can be rearranged in 3! ways

Total arrangements = 2!*3!*3! = 2*6*6 = 72

Answer: Option C
_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

Veritas Prep GMAT Instructor
User avatar
D
Joined: 16 Oct 2010
Posts: 8888
Location: Pune, India
Re: In how many different ways can 3 boys and 3 girls be seated in a row  [#permalink]

Show Tags

New post 04 Jan 2017, 05:22
2
Bunuel wrote:
In how many different ways can 3 boys and 3 girls be seated in a row of 6 chairs such that the girls are not separated, and the boys are not separated?

A. 24
B. 36
C. 72
D. 144
E. 288


Bunch up the boys together and the girls together. Now we have to arrange 2 groups which we can do in 2! ways.

The boys within themselves can be arranged in 3! ways and the girls within themselves can be arranged in 3! ways.

Total arrangements = 2 * 3! * 3! = 72

Answer (C)

For more on arrangements with constraints, check:
https://www.veritasprep.com/blog/2011/1 ... ts-part-i/
https://www.veritasprep.com/blog/2011/1 ... s-part-ii/
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

Intern
Intern
User avatar
Joined: 24 Jun 2016
Posts: 31
GMAT ToolKit User
Re: In how many different ways can 3 boys and 3 girls be seated in a row  [#permalink]

Show Tags

New post 04 Jan 2017, 20:45
Condition: girls not separated..and boys are not separated

Count them as 1&1. Now we have 1boys n 1girl..

Arrangements =2!
And arrangements inside 3 girls & inside 3boys is=3! & 3!

Total=2!*3!*3! = 72 option C

Sent from my MotoG3 using GMAT Club Forum mobile app
Target Test Prep Representative
User avatar
P
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 4947
Location: United States (CA)
Re: In how many different ways can 3 boys and 3 girls be seated in a row  [#permalink]

Show Tags

New post 06 Jan 2017, 09:57
Bunuel wrote:
In how many different ways can 3 boys and 3 girls be seated in a row of 6 chairs such that the girls are not separated, and the boys are not separated?

A. 24
B. 36
C. 72
D. 144
E. 288


We need to determine how many ways to arrange 3 boys and 3 girls in a row of six chairs when the boys must be seated together and the girls must be seated together. Since order matters, we have a permutation problem.

We can arrange the boys and girls as follows:

[B1)-B2)-B(3)] - [G(1)-G(2)-G(3)]

(Note: Since the boys must sit together and the girls must sit together, we have included the boys in one bracket and the girls in one bracket.)

Since we have 2 brackets, we can arrange those 2 brackets in 2! or 2 ways. However, we must account for the individual arrangements of the boys and the girls. The boys can be arranged in 3! or 6 ways and the girls can be arranged in 3! or 6 ways. Thus, the group can be arranged in 2 x 6 x 6 = 72 ways.

Answer: C
_________________

Scott Woodbury-Stewart
Founder and CEO

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

EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 13562
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: In how many different ways can 3 boys and 3 girls be seated in a row  [#permalink]

Show Tags

New post 26 Mar 2018, 12:34
1
Hi Al,

There are a number of ways to do the "math in this question", but here's a way that you might find easy:

The fact that we have 6 chairs in a row means that we'll likely be doing a permutation. We're given the specific rule that the seating will have to be either GGGBBB or BBBGGG.

The first chair can have either a boy or a girl:

6 _ _ _ _ _

Whether it's a boy or a girl, the next two chairs must be the same gender:

6 2 1 _ _ _

Then the next 3 chairs must be the other gender:

6 2 1 3 2 1

Now multiply:

6x2x1x3x2x1 = 72 possibilities.

Final Answer:

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

Co-Founder & 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!*****

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 9871
Premium Member
Re: 3 boys and 3 girls  [#permalink]

Show Tags

New post 09 Sep 2018, 10:22
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 Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

GMAT Club Bot
Re: 3 boys and 3 girls   [#permalink] 09 Sep 2018, 10:22
Display posts from previous: Sort by

In how many different ways can 3 boys and 3 girls be seated in a row

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.