It is currently 22 Nov 2017, 19:33

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

Events & Promotions in June
Open Detailed Calendar

Six children — A, B, C, D, E, and F — are going to sit in six chairs i

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

Hide Tags

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42305

Kudos [?]: 133076 [0], given: 12403

Six children — A, B, C, D, E, and F — are going to sit in six chairs i [#permalink]

Show Tags

New post 04 Mar 2015, 04:35
Expert's post
8
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

72% (00:55) correct 28% (01:16) wrong based on 168 sessions

HideShow timer Statistics

Six children — A, B, C, D, E, and F — are going to sit in six chairs in a row. Child E must be somewhere to the left of child F. How many possible configurations are there for the children?

A. 60
B. 180
C. 240
D. 360
E. 720



Kudos for a correct solution.
[Reveal] Spoiler: OA

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 133076 [0], given: 12403

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42305

Kudos [?]: 133076 [0], given: 12403

Re: Six children — A, B, C, D, E, and F — are going to sit in six chairs i [#permalink]

Show Tags

New post 04 Mar 2015, 04:39
Bunuel wrote:
Six children — A, B, C, D, E, and F — are going to sit in six chairs in a row. Child E must be somewhere to the left of child F. How many possible configurations are there for the children?

A. 60
B. 180
C. 240
D. 360
E. 720



Kudos for a correct solution.



Similar yet different questions:
seven-children-a-b-c-d-e-f-and-g-are-going-to-sit-in-seven-c-194099.html
seven-children-a-b-c-d-e-f-and-g-are-going-to-sit-in-seven-c-194097.html
seven-children-a-b-c-d-e-f-and-g-are-going-to-sit-in-seven-c-194096.html
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 133076 [0], given: 12403

Senior Manager
Senior Manager
avatar
Joined: 27 Dec 2013
Posts: 303

Kudos [?]: 39 [0], given: 113

Re: Six children — A, B, C, D, E, and F — are going to sit in six chairs i [#permalink]

Show Tags

New post 04 Mar 2015, 11:50
1
This post was
BOOKMARKED
Hi Bunuel,

I am getting the answer 220.

My answer is as follows,

F cannot be in first position:

If F is in second position; then E must be in First position- Remaining 4 children can be arranged in 4! ways= 24

If F is in Third position; then E can be two places, If we select 1 letter for left of F, then we will have 4C1X2X3=24

If F is in fourth position, then E can be in three places, So we have 4C2X3X2= 36

If F is in fifth position, then E can be in 4 places, 4c3X4X1= 16

If F is in sixth position, then we have 5! wasys= 120.

Summing all, I am getting 220 ways. Please highlight me where I am going wrong.

Bunuel wrote:
Six children — A, B, C, D, E, and F — are going to sit in six chairs in a row. Child E must be somewhere to the left of child F. How many possible configurations are there for the children?

A. 60
B. 180
C. 240
D. 360
E. 720



Kudos for a correct solution.

_________________

Kudos to you, for helping me with some KUDOS.

Kudos [?]: 39 [0], given: 113

1 KUDOS received
Intern
Intern
avatar
Joined: 15 Feb 2015
Posts: 1

Kudos [?]: 1 [1], given: 0

Re: Six children — A, B, C, D, E, and F — are going to sit in six chairs i [#permalink]

Show Tags

New post 04 Mar 2015, 12:18
1
This post received
KUDOS
Hi,

I am getting the answer as 360.

My answer is as follows,

F is in first position from the right, then the rest 5 positions can be filled in 5! ways=120

If F is in Second position; then the first position can be filled in 4 ways, and the rest 4 positions in 4! ways; i.e. 24*4=96

If F is in Third position; then the first and second position can be filled in 4 and 3 ways, and the rest 3 positions in 3! ways; i.e. 4*3*3!=72

If F is in Fourth position; then the first, second and the third position can be filled in 4, 3, and 2 ways ways, and the rest 2 positions in 2! ways; i.e. 4*3*2*2!=48

If F is in Fifth position; then the first, second third and the fourth position can be filled in 4, 3, 2 and 1 way, and the rest 1positions in 1! ways; i.e. 4!=24

Hence, answer should be 360.

Thanks
Bunuel wrote:
Six children — A, B, C, D, E, and F — are going to sit in six chairs in a row. Child E must be somewhere to the left of child F. How many possible configurations are there for the children?

A. 60
B. 180
C. 240
D. 360
E. 720



Kudos for a correct solution.
[/quote]

Kudos [?]: 1 [1], given: 0

9 KUDOS received
Manager
Manager
avatar
Joined: 13 Dec 2013
Posts: 59

Kudos [?]: 34 [9], given: 34

Location: Iran (Islamic Republic of)
GMAT ToolKit User
Re: Six children — A, B, C, D, E, and F — are going to sit in six chairs i [#permalink]

Show Tags

New post 04 Mar 2015, 12:42
9
This post received
KUDOS
1
This post was
BOOKMARKED
The answer is D.... But, the way to reach to the correct answer is not as long as according to some guys !!!


Here is a simple rule ... First count the order of sitting people in row without any restriction....


As notice 6 people sitting in a ROW , so with no restriction the total number of arranging for 6 people is 6! = 720 ways.


So, in this step, lets apply the restriction ... restriction is that E must sit some where in the left of F...

Very simple rule : in these cases ONLY divide the total number of arrangement to 2 !!!! because in HALF of the cases E can sit in the left of F...

So the total number of arrangement is : 720/2 = 360 .... answer D


IMPORTANT notice : IF the problem said the 6 guys wanted to sit IN A CIRCULAR TABLE OR some thing like that, the total number of arrangement would be (6-1) = 5! = 120 and then 120/2

=60 :lol: :lol: :lol: :lol:

Kudos [?]: 34 [9], given: 34

3 KUDOS received
Intern
Intern
avatar
Joined: 13 Aug 2013
Posts: 46

Kudos [?]: 60 [3], given: 44

GMAT ToolKit User
Re: Six children — A, B, C, D, E, and F — are going to sit in six chairs i [#permalink]

Show Tags

New post 04 Mar 2015, 12:46
3
This post received
KUDOS
1
This post was
BOOKMARKED
IMO D
Let us take a smaller example. Consider only A, B, C and assume that we need to find all possible arrangements when A is somewhere to the left of B.

All possible combinations: ABC, ACB, BAC, BCA, CAB, CBA

As you can see, exactly three of the cases are such when A is to the left of B. Meaning, half of the times, A will be to left of B. We can generalize this rule for A, B, C, D and we will find that in exactly 12 arrangements, A will be to the left of B.

Using the same concept here, we have six kids, so in all = \(6!\) i.e. \(720\) arrangements possible. Among these \(720\) combinations half of the times E will be somewhere to the left of F. Hence \(360\)
_________________

Kudos plz if it helped

Kudos [?]: 60 [3], given: 44

1 KUDOS received
Manager
Manager
User avatar
Joined: 27 Jun 2014
Posts: 75

Kudos [?]: 51 [1], given: 125

Location: New Zealand
Concentration: Strategy, General Management
GMAT 1: 710 Q43 V45
GRE 1: 324 Q161 V163
GRE 2: 325 Q159 V166
GPA: 3.6
WE: Editorial and Writing (Computer Software)
Premium Member
Re: Six children — A, B, C, D, E, and F — are going to sit in six chairs i [#permalink]

Show Tags

New post 04 Mar 2015, 19:11
1
This post received
KUDOS
Bunuel wrote:
Six children — A, B, C, D, E, and F — are going to sit in six chairs in a row. Child E must be somewhere to the left of child F. How many possible configurations are there for the children?

A. 60
B. 180
C. 240
D. 360
E. 720



Kudos for a correct solution.


A smart question that tests your presence of mind more than ability to count. Six students can be arranged in 6! ways, which gives us 720 arrangements. Of these, 360 arrangements will be such that E is to the left of F and the remaining 360 will have E to the right. Answer is D.
_________________

"Hardwork is the easiest way to success." - Aviram

One more shot at the GMAT...aiming for a more balanced score.

Kudos [?]: 51 [1], given: 125

Expert Post
2 KUDOS received
Veritas Prep GMAT Instructor
User avatar
G
Joined: 16 Oct 2010
Posts: 7745

Kudos [?]: 17853 [2], given: 235

Location: Pune, India
Re: Six children — A, B, C, D, E, and F — are going to sit in six chairs i [#permalink]

Show Tags

New post 04 Mar 2015, 21:52
2
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
Bunuel wrote:
Six children — A, B, C, D, E, and F — are going to sit in six chairs in a row. Child E must be somewhere to the left of child F. How many possible configurations are there for the children?

A. 60
B. 180
C. 240
D. 360
E. 720



Kudos for a correct solution.


Here is a post detailing the symmetry principle: http://www.veritasprep.com/blog/2011/10 ... s-part-ii/

Using the symmetry principle, you say that number of possible configurations = 6!/2 = 360

Answer (D)
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

Kudos [?]: 17853 [2], given: 235

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42305

Kudos [?]: 133076 [0], given: 12403

Re: Six children — A, B, C, D, E, and F — are going to sit in six chairs i [#permalink]

Show Tags

New post 08 Mar 2015, 14:29
Bunuel wrote:
Six children — A, B, C, D, E, and F — are going to sit in six chairs in a row. Child E must be somewhere to the left of child F. How many possible configurations are there for the children?

A. 60
B. 180
C. 240
D. 360
E. 720



Kudos for a correct solution.


MAGOOSH OFFICIAL SOLUTION:

If we wanted, we could make this one extremely difficult, counting out all kinds of possibilities in several different cases. Instead, we are going to make this ridiculously easy.

First of all, with absolutely no restrictions, how many ways can the six children be arranged on the six chairs? That’s a permutation of the 6 items —- 6P6 = 6! = 720. That’s the total number of arrangements with no restrictions. Of course, those 720 arrangements have all kinds of symmetry to them. In particular, in all of those arrangements overall, it’s just as likely for E to be to the left of F as it is for E to be to the right of F. Therefore, exactly half must have E to the right of F, and exactly half must have E to the left of F. Therefore, exactly (1/2)*720 = 360 of the arrangements have E to the left of F.

Answer = D.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 133076 [0], given: 12403

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 15546

Kudos [?]: 283 [0], given: 0

Premium Member
Re: Six children — A, B, C, D, E, and F — are going to sit in six chairs i [#permalink]

Show Tags

New post 11 Oct 2017, 04:58
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

Kudos [?]: 283 [0], given: 0

Re: Six children — A, B, C, D, E, and F — are going to sit in six chairs i   [#permalink] 11 Oct 2017, 04:58
Display posts from previous: Sort by

Six children — A, B, C, D, E, and F — are going to sit in six chairs i

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


GMAT Club MBA Forum Home| About| Terms and Conditions| 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®.