NEW HERE? LEARN MORE
closeclose
Last visit was: 25 Apr 2024, 15:00 It is currently 25 Apr 2024, 15:00
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

7 people (A, B, C, D, E, F and G) go to a movie and sit

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
avatar
megatron13
Intern
Intern
Joined: 17 Jul 2013
Posts: 44
Own Kudos [?]: 151 [82]
Given Kudos: 19
Schools: HBS '18 (A) Yale '18 (D)
GMAT 1: 710 Q49 V38
GRE 1: Q166 V160
GPA: 3.74
Send PM
7 people (A, B, C, D, E, F and G) go to a movie and sit [#permalink] New post   05 Sep 2014, 13:02
5
Kudos
77
Bookmarks
00:00
A
B
C
D
E

Difficulty:

95% (hard)

Question Stats:

26% (02:08) correct 74% (01:38) wrong based on 534 sessions
Hide Show timer Statistics
7 people (A, B, C, D, E, F and G) go to a movie and sit next to each other in 7 adjacent seats in the front row of the theater.

How many different arrangements are possible? If A will not sit to the left of F and F will not sit to the left of E. How many different arrangements are possible.

A) 7!/2
B) 7!/3
C) 7!/4
D) 7!/5
E) 7!/6
ShowHide Answer
Official Answer
E
Most Helpful Reply
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92915
Own Kudos [?]: 619016 [26]
Given Kudos: 81595
Send PM
CAT Tests Forum Quiz Mode
Re: 7 people (A, B, C, D, E, F and G) go to a movie and sit [#permalink] New post   05 Sep 2014, 13:28
8
Kudos
18
Bookmarks
Expert Reply
megatron13 wrote:
7 people (A, B, C, D, E, F and G) go to a movie and sit next to each other in 7 adjacent seats in the front row of the theater.

How many different arrangements are possible? If A will not sit to the left of F and F will not sit to the left of E. How many different arrangements are possible.

A) 7!/2
B) 7!/3
C) 7!/4
D) 7!/5
E) 7!/6


7 people can be arranged in a row in 7! ways.

Now, three people among those 7 can be arranged in 3! = 6 ways:
AFE
AEF
EAF
EFA
FAE
FEA

From the 6 arrangements above only EFA is possible (A is not to the left of F and F is not to the left of E), so out of total 7! ways only in 1/6th of the arrangements they are sitting as they want.

Answer: E (7!/6).
General Discussion
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92915
Own Kudos [?]: 619016 [4]
Given Kudos: 81595
Send PM
CAT Tests Forum Quiz Mode
Re: 7 people (A, B, C, D, E, F and G) go to a movie and sit [#permalink] New post   05 Sep 2014, 13:30
4
Bookmarks
Expert Reply
megatron13 wrote:
7 people (A, B, C, D, E, F and G) go to a movie and sit next to each other in 7 adjacent seats in the front row of the theater.

How many different arrangements are possible? If A will not sit to the left of F and F will not sit to the left of E. How many different arrangements are possible.

A) 7!/2
B) 7!/3
C) 7!/4
D) 7!/5
E) 7!/6


Similar questions to practice:
mother-mary-comes-to-me-86407.html (or: mary-and-joe-126407.html);
six-mobsters-have-arrived-at-the-theater-for-the-premiere-of-the-126151.html
in-how-many-different-ways-can-the-letters-a-a-b-91460.html
goldenrod-and-no-hope-are-in-a-horse-race-with-6-contestants-82214.html
meg-and-bob-are-among-the-5-participants-in-a-cycling-race-58095.html
avatar
megatron13
Intern
Intern
Joined: 17 Jul 2013
Posts: 44
Own Kudos [?]: 151 [0]
Given Kudos: 19
Schools: HBS '18 (A) Yale '18 (D)
GMAT 1: 710 Q49 V38
GRE 1: Q166 V160
GPA: 3.74
Send PM
Re: 7 people (A, B, C, D, E, F and G) go to a movie and sit [#permalink] New post   06 Sep 2014, 02:35
Hi Bunuel,

I am having difficulty understanding this approach since there can be combinations in which other people might sit between A, F and E. For this question, I was trying to count all the invalid combinations and subtract from total combinations. But how to count invalid cases like below

A,_,_,F,_E,_ or _,F,_,E,_,_,A
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92915
Own Kudos [?]: 619016 [0]
Given Kudos: 81595
Send PM
CAT Tests Forum Quiz Mode
Re: 7 people (A, B, C, D, E, F and G) go to a movie and sit [#permalink] New post   06 Sep 2014, 09:23
Expert Reply
megatron13 wrote:
Hi Bunuel,

I am having difficulty understanding this approach since there can be combinations in which other people might sit between A, F and E. For this question, I was trying to count all the invalid combinations and subtract from total combinations. But how to count invalid cases like below

A,_,_,F,_E,_ or _,F,_,E,_,_,A


When I say AFE or AEF I don't mean that they are necessarily adjacent, there might be other people between them.
avatar
B
Zizad
Intern
Intern
Joined: 24 Jun 2012
Posts: 40
Own Kudos [?]: 6 [0]
Given Kudos: 2
Location: India
Concentration: Strategy, General Management
Schools: Kellogg '19 (D) Duke '19 (WL) Goizueta '19 (A$) McCombs '19 (A$) Mays '19 (A) McDonough '19 (A) Johnson '19 (D) Kelley '19 (A)
GMAT 1: 730 Q47 V42
Send PM
GMAT ToolKit User Reviews Badge
7 people (A, B, C, D, E, F and G) go to a movie and sit [#permalink] New post   Updated on: 01 May 2016, 01:06
Hi Bunuel,


When I apply symmetry here the answer becomes (1/2) * (1/2) * (7!) = 7!/4. What am I doing incorrectly here? Could you please help me out. Thank you.

Regards,
Zizad

Originally posted by Zizad on 25 Sep 2015, 14:37.
Last edited by Zizad on 01 May 2016, 01:06, edited 1 time in total.
User avatar
AryamaDuttaSaikia
Jamboree GMAT Instructor
Joined: 15 Jul 2015
Status:GMAT Expert
Affiliations: Jamboree Education Pvt Ltd
Posts: 252
Own Kudos [?]: 654 [3]
Given Kudos: 1
Location: India
Send PM
Re: 7 people (A, B, C, D, E, F and G) go to a movie and sit [#permalink] New post   29 Sep 2015, 23:17
2
Kudos
1
Bookmarks
In this case, A not left of F (means A right of F) and F not left of E (means F right of E). There is a common element F and both the conditions need to be satisfied. (A right of F and F right of E). So, the concept of symmetry overlooks this common bit and thus different answer.

Out of the three elements(A,F,E). Only one of the arrangement sufficies this aspect so 7!*(1/6)

Hope this helps.
User avatar
L
chetan2u
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11178
Own Kudos [?]: 31932 [2]
Given Kudos: 290
Send PM
Reviews Badge
Re: 7 people (A, B, C, D, E, F and G) go to a movie and sit [#permalink] New post   17 May 2016, 20:57
1
Kudos
1
Bookmarks
Expert Reply
megatron13 wrote:
7 people (A, B, C, D, E, F and G) go to a movie and sit next to each other in 7 adjacent seats in the front row of the theater.

How many different arrangements are possible? If A will not sit to the left of F and F will not sit to the left of E. How many different arrangements are possible.

A) 7!/2
B) 7!/3
C) 7!/4
D) 7!/5
E) 7!/6


Hi debbiem,

Refer your PM..

For doing any of these Qs, the MEANING is most important..
what does ---- A will not sit to the left of F and F will not sit to the left of E -- mean.
Keep in mind- it does not talk of immediate left..

so If I have a combination like
D,A,C,F,B,E,G.....
we are concerned about the position of A, F and E.. they have to be in ...E..F..A..
so If we keep the position of all other B,C,D, and G constant these 3- E,F and A can be arranged in 3! ways and ONLY one way ...E..F..A.. is correct
so ONLY 1 out of 3! or 6...OR 1/6 are VALID
Same will be the case for all other arrangements of B,C,D, and G ..
so our answer will be TOTAL *VALID = 7!*1/6 = 7!/6....
User avatar
L
KarishmaB
Tutor
Joined: 16 Oct 2010
Posts: 14823
Own Kudos [?]: 64922 [3]
Given Kudos: 426
Location: Pune, India
Send PM
Re: 7 people (A, B, C, D, E, F and G) go to a movie and sit [#permalink] New post   18 May 2016, 01:50
1
Kudos
2
Bookmarks
Expert Reply
Zizad wrote:
Hi Bunuel,


When I apply symmetry here the answer becomes (1/2) * (1/2) * (7!) = 7!/4. What am I doing incorrectly here? Could you please help me out. Thank you.

Regards,
Zizad


Another way to explain why you cannot use symmetry:

A will be to the right of F and F will be to the right of E. So it looks like

E ---- F ---- A

Here, A also has a relation with E - it cannot be to the left of E. Symmetry works when dealing with independent cases.

Check this post for the symmetry discussion:
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2011/10 ... s-part-ii/
User avatar
B
unicornilove
Manager
Manager
Joined: 23 Jan 2024
Posts: 73
Own Kudos [?]: 7 [0]
Given Kudos: 109
Send PM
CAT Tests
Re: 7 people (A, B, C, D, E, F and G) go to a movie and sit [#permalink] New post   14 Mar 2024, 22:52
Understood for the range of ways for AFE, only 1 out of 6 options work.

How does this translate to the answer though? I saw that you said later in the posts that you have also included e.g. A _ _ F _ E. How does that work?
Bunuel wrote:
megatron13 wrote:
7 people (A, B, C, D, E, F and G) go to a movie and sit next to each other in 7 adjacent seats in the front row of the theater.

How many different arrangements are possible? If A will not sit to the left of F and F will not sit to the left of E. How many different arrangements are possible.

A) 7!/2
B) 7!/3
C) 7!/4
D) 7!/5
E) 7!/6

7 people can be arranged in a row in 7! ways.

Now, three people among those 7 can be arranged in 3! = 6 ways:
AFE
AEF
EAF
EFA
FAE
FEA

From the 6 arrangements above only EFA is possible (A is not to the left of F and F is not to the left of E), so out of total 7! ways only in 1/6th of the arrangements they are sitting as they want.

Answer: E (7!/6).

­
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92915
Own Kudos [?]: 619016 [0]
Given Kudos: 81595
Send PM
CAT Tests Forum Quiz Mode
Re: 7 people (A, B, C, D, E, F and G) go to a movie and sit [#permalink] New post   15 Mar 2024, 00:56
Expert Reply
unicornilove wrote:
Understood for the range of ways for AFE, only 1 out of 6 options work.

How does this translate to the answer though? I saw that you said later in the posts that you have also included e.g. A _ _ F _ E. How does that work?
Bunuel wrote:
megatron13 wrote:
7 people (A, B, C, D, E, F and G) go to a movie and sit next to each other in 7 adjacent seats in the front row of the theater.

How many different arrangements are possible? If A will not sit to the left of F and F will not sit to the left of E. How many different arrangements are possible.

A) 7!/2
B) 7!/3
C) 7!/4
D) 7!/5
E) 7!/6

7 people can be arranged in a row in 7! ways.

Now, three people among those 7 can be arranged in 3! = 6 ways:
AFE
AEF
EAF
EFA
FAE
FEA

From the 6 arrangements above only EFA is possible (A is not to the left of F and F is not to the left of E), so out of total 7! ways only in 1/6th of the arrangements they are sitting as they want.

Answer: E (7!/6).

­

­
I'll try once more. Three people, A, F, and E, can be arranged in 3! = 6 ways. Out of these 6 arrangements, only one, EFA, satisfies the restriction, making it 1/6. Thus, out of the total 7! arrangements, only one-sixth of them satisfies the restriction.
User avatar
B
unicornilove
Manager
Manager
Joined: 23 Jan 2024
Posts: 73
Own Kudos [?]: 7 [0]
Given Kudos: 109
Send PM
CAT Tests
Re: 7 people (A, B, C, D, E, F and G) go to a movie and sit [#permalink] New post   16 Mar 2024, 02:22
Hi Bunuel, thanks for the explanation. I understand that. However, aren't you missing the cases where they fit the requirement but not directly next to each other?
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92915
Own Kudos [?]: 619016 [0]
Given Kudos: 81595
Send PM
CAT Tests Forum Quiz Mode
Re: 7 people (A, B, C, D, E, F and G) go to a movie and sit [#permalink] New post   16 Mar 2024, 02:39
Expert Reply
unicornilove wrote:
Hi Bunuel, thanks for the explanation. I understand that. However, aren't you missing the cases where they fit the requirement but not directly next to each other?


­No, we haven't overlooked any cases there. Each of the six arrangements of A, F, and E is relative to each other. However, within each arrangement, there might be additional people positioned among them.
GMAT Club Bot
gmatclubot
Re: 7 people (A, B, C, D, E, F and G) go to a movie and sit [#permalink]
16 Mar 2024, 02:39
Moderators:
Bunuel
Math Expert
92915 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