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

It is currently 15 Nov 2018, 01:16

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 November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
  • Free GMAT Strategy Webinar

     November 17, 2018

     November 17, 2018

     07:00 AM PST

     09:00 AM PST

    Nov. 17, 7 AM PST. Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.
  • GMATbuster's Weekly GMAT Quant Quiz # 9

     November 17, 2018

     November 17, 2018

     09:00 AM PST

     11:00 AM PST

    Join the Quiz Saturday November 17th, 9 AM PST. The Quiz will last approximately 2 hours. Make sure you are on time or you will be at a disadvantage.

In how many ways can Ann, Bob, Chuck, Don and Ed be seated

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

Hide Tags

Senior Manager
Senior Manager
avatar
Status: Do and Die!!
Joined: 15 Sep 2010
Posts: 271
In how many ways can Ann, Bob, Chuck, Don and Ed be seated  [#permalink]

Show Tags

New post 25 Nov 2010, 18:06
7
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

60% (01:17) correct 40% (01:34) wrong based on 214 sessions

HideShow timer Statistics

In how many ways can Ann, Bob, Chuck, Don and Ed be seated in a row such that Ann and Bob are not seated next to each other?

A. 24
B. 48
C. 56
D. 72
E. 96

_________________

I'm the Dumbest of All !!

Most Helpful Expert Reply
Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8531
Location: Pune, India
Re: In how many ways can Ann, Bob, Chuck, Don and Ed be seated  [#permalink]

Show Tags

New post 25 Nov 2010, 20:55
4
6
shrive555 wrote:
In how many ways can Ann, Bob, Chuck, Don and Ed be seated in a row such that Ann and Bob are not seated next to each other?

24
48
56
72
96


When the constraint on an arrangement says, "Two people should not be seated together," we do just the opposite. We make them sit together! Kind of tie them with a thread and assume they are one unit!
Let's see why....

These 5 people can be arranged in 5! ways. These are the total number of ways you get.
Now, when we tie 2 people together, we have only 4 entities to arrange. We can do this in 4! ways. But in each of these entities, the two people can sit in two different ways (AB and BA). So number of ways in which these two people sit together is 4!*2!.

Now, the ways in which these two people will not be together will be 5!- 4!*2! = 4!(5 - 2) = 72
_________________

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 >

GMAT self-study has never been more personalized or more fun. Try ORION Free!

General Discussion
Manager
Manager
avatar
Joined: 27 Jul 2010
Posts: 161
Location: Prague
Schools: University of Economics Prague
GMAT ToolKit User
Re: In how many ways can Ann, Bob, Chuck, Don and Ed be seated  [#permalink]

Show Tags

New post 26 Nov 2010, 12:22
my solution:

3! * 6*2 = 72

3! for Chuck, Don and Ed

6 positions for Ann and Bob: AC AD AE BC BE CE * 2 (as they can switch they positions)

It is not as concise as Karishma's but it works.
_________________

You want somethin', go get it. Period!

Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8531
Location: Pune, India
Re: In how many ways can Ann, Bob, Chuck, Don and Ed be seated  [#permalink]

Show Tags

New post 27 Nov 2010, 13:13
craky wrote:
my solution:

3! * 6*2 = 72

3! for Chuck, Don and Ed

6 positions for Ann and Bob: AC AD AE BC BE CE * 2 (as they can switch they positions)

It is not as concise as Karishma's but it works.


Yes, your logic is absolutely fine. If the number of people is manageable, we can directly find the number of ways in which the two of them should not be seated together.
You arranged C, D and E in 3! ways.
Attachment:
Ques2.jpg
Ques2.jpg [ 3.56 KiB | Viewed 6681 times ]


The 4 dots show 4 positions for Ann.When Ann occupies one of these positions, 3 positions are left over for Bob. So Ann and Bob can sit in 4*3 = 12 ways.
Total 3! * 12 = 72 ways.
_________________

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 >

GMAT self-study has never been more personalized or more fun. Try ORION Free!

SVP
SVP
avatar
B
Joined: 06 Nov 2014
Posts: 1882
Re: In how many ways can Ann, Bob, Chuck, Don and Ed be seated  [#permalink]

Show Tags

New post 13 Oct 2015, 19:24
tuanquang269 wrote:
In how many ways can Ann, Bob, Chuck, Don and Ed be seated in a row such that Ann and Bob are not seated next to each other?

(A) 24

(B) 58

(C) 56

(D) 72

(E) 96


In these types of questions, always try to subtract the not allowed arrangements from the total arrangements. This makes our lives much easier.
Here we will assume that Ann and Bob always sit together i.e. they are a single entity
Total arrangements: 5!

Arrangements in which Ann and Bob sit together = 4!*2!
We get this because, total arrangements =4! and Ann and Bob can be arranged in 2! ways

Subtracting this from the total: 5! - 4!*2! = 72. Option D
Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830
Re: In how many ways can Ann, Bob, Chuck, Don and Ed be seated  [#permalink]

Show Tags

New post 19 Apr 2017, 15:02
1
1
shrive555 wrote:
In how many ways can Ann, Bob, Chuck, Don and Ed be seated in a row such that Ann and Bob are not seated next to each other?

A. 24
B. 48
C. 56
D. 72
E. 96


We can use the following formula:

Total number of ways to arrange the 5 people = (number of arrangements when Bob sits next to Ann) + (number of arrangements when Bob does not sit next to Ann)

Let’s determine the number of arrangements when Bob sits next to Ann.

We can denote Ann, Bob, Chuck, Don, and Ed as A, B, C, D, and E, respectively.

If Ann and Bob must sit together, we can consider them as one person [AB]. For example, one seating arrangement could be [AB][C][D][E]. Thus, the number of ways to arrange four people in a row is 4! = 24.

However, we must also account for the ways we can arrange Ann and Bob, that is, either [AB] or [BA]. Thus, there are 2! = 2 ways to arrange Ann and Bob.

Therefore, the total number of seating arrangements is 24 x 2 = 48 if Ann and Bob DO sit next to each other.

Since there are 5 people being arranged, the total number of possible arrangements is 5! = 120.

Thus, the number of arrangements when Bob does NOT sit next to Ann is 120 - 48 = 72.

Answer: D
_________________

Jeffery Miller
Head of GMAT Instruction

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

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 8775
Premium Member
Re: In how many ways can Ann, Bob, Chuck, Don and Ed be seated  [#permalink]

Show Tags

New post 21 Jul 2018, 08:21
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: In how many ways can Ann, Bob, Chuck, Don and Ed be seated &nbs [#permalink] 21 Jul 2018, 08:21
Display posts from previous: Sort by

In how many ways can Ann, Bob, Chuck, Don and Ed be seated

  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®.