Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 04 Apr 2010
Posts: 161

A group consisting of N couples are going to see a movie. [#permalink]
Show Tags
22 Mar 2011, 20:50
4
This post received KUDOS
10
This post was BOOKMARKED
Question Stats:
47% (02:12) correct
53% (01:13) wrong based on 393 sessions
HideShow timer Statistics
A group consisting of N couples are going to see a movie. The seats in each row of the theater is greater than 2N. If the group decides to all sit in the same row, each couple is indifferent to empty seats next to them, and each couple insists on sitting together, how many seating arrangements are possible? (1) N = 5 (2) The group will all sit next to one another, starting with the first seat in the row.
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Consider me giving KUDOS, if you find my post helpful. If at first you don't succeed, you're running about average. ~Anonymous



Director
Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
Joined: 03 Feb 2011
Posts: 899

Re: A group consisting of N couples are going to see a movie. [#permalink]
Show Tags
22 Mar 2011, 21:18
First I thought s1 is sufficient but on taking a closer look the statement said greater than 2N seats. Hence C is sufficient. You have only three answers a,c or worst case e. If this question turns out to be your 3137 question take a moment to think why answer may not be E.
If the seats would have been Exactly 2N the answer is A. Please correct if the reasoning has flaw
Posted from my mobile device



Manager
Joined: 04 Apr 2010
Posts: 161

Re: A group consisting of N couples are going to see a movie. [#permalink]
Show Tags
22 Mar 2011, 21:32
1
This post received KUDOS
Seats in each row greater than 2N brings possibility to increase no be seats in a row up to 100 to 1000 to millions. However N could be 2, 4 , 6. There could be 1 or 50 or 100 or .. seats gap between each couple.Any number of arrangement is possible. Please correct me !
_________________
Consider me giving KUDOS, if you find my post helpful. If at first you don't succeed, you're running about average. ~Anonymous



Math Forum Moderator
Joined: 20 Dec 2010
Posts: 2010

Re: A group consisting of N couples are going to see a movie. [#permalink]
Show Tags
22 Mar 2011, 21:46
1
This post received KUDOS
1
This post was BOOKMARKED
gmat1220 wrote: First I thought s1 is sufficient but on taking a closer look the statement said greater than 2N seats. Hence C is sufficient. You have only three answers a,c or worst case e. If this question turns out to be your 3137 question take a moment to think why answer may not be E.
If the seats would have been Exactly 2N the answer is A. Please correct if the reasoning has flaw
Posted from my mobile device You are right; if the seats were exactly 2N, the arrangements would be = 5!*(2)^5 and "A" would have sufficed. St2 tells us that they are all seating together without any gaps starting with the FIRST seat, which now means that they are indeed occupying first 10 seats of the row and the rest of the seats become immaterial and makes "C" sufficient. Ans: "C"
_________________
~fluke
GMAT Club Premium Membership  big benefits and savings



Manager
Joined: 27 May 2008
Posts: 126

Re: A group consisting of N couples are going to see a movie. [#permalink]
Show Tags
22 Mar 2011, 22:59
@bhandariavi: Can you tell me the source of this question???



SVP
Joined: 16 Nov 2010
Posts: 1663
Location: United States (IN)
Concentration: Strategy, Technology

Re: A group consisting of N couples are going to see a movie. [#permalink]
Show Tags
22 Mar 2011, 23:09
1
This post was BOOKMARKED
@fluke  "if the seats were exactly 2N, the arrangements would be = 5!*(2)^5 " Is it something like  5 couples in 5 pairs of seats = 5! and then 2 persons in each of the 5 couples can be arranged among themselves as 2! So total 5! * (2!)^5 = 5! * (2)^5
_________________
Formula of Life > Achievement/Potential = k * Happiness (where k is a constant)
GMAT Club Premium Membership  big benefits and savings



Math Forum Moderator
Joined: 20 Dec 2010
Posts: 2010

Re: A group consisting of N couples are going to see a movie. [#permalink]
Show Tags
22 Mar 2011, 23:37
subhashghosh wrote: @fluke  "if the seats were exactly 2N, the arrangements would be = 5!*(2)^5 "
Is it something like  5 couples in 5 pairs of seats = 5!
and then 2 persons in each of the 5 couples can be arranged among themselves as 2!
So total 5! * (2!)^5
= 5! * (2)^5 Precisely!!! If you adhere all the couples and make them one unit each; there are 5 units; 5 units can be arranged in 5! ways And within the unit; every couple can rearrange in 2! ways.
_________________
~fluke
GMAT Club Premium Membership  big benefits and savings



Manager
Joined: 04 Nov 2012
Posts: 60

Re: A group consisting of N couples are going to see a movie. [#permalink]
Show Tags
15 Apr 2013, 07:29
Please help.
If the seats are more than 2N, there is no upper limit.
So, if we use the counting principle, depending on the value of 2N, the number of options available to the first couple could be 100, 1000 or whatever. SUbesquent couples would be limited by where the first couple chose to sit.
In this case, shouldn.t the answer be E?



Math Expert
Joined: 02 Sep 2009
Posts: 39759

Re: A group consisting of N couples are going to see a movie. [#permalink]
Show Tags
15 Apr 2013, 07:37
12bhang wrote: Please help.
If the seats are more than 2N, there is no upper limit.
So, if we use the counting principle, depending on the value of 2N, the number of options available to the first couple could be 100, 1000 or whatever. SUbesquent couples would be limited by where the first couple chose to sit.
In this case, shouldn.t the answer be E? Take a closer look at the second statement: The group will all sit next to one another, starting with the first seat in the row.
_________________
New to the Math Forum? Please read this: 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? Extrahard Quant Tests with Brilliant Analytics



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16035

Re: A group consisting of N couples are going to see a movie. [#permalink]
Show Tags
01 Oct 2014, 02:46
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



Intern
Status: Don't Give Up!
Joined: 15 Aug 2014
Posts: 33
Location: India
Concentration: Operations, General Management
GMAT Date: 04252015
WE: Engineering (Manufacturing)

Re: A group consisting of N couples are going to see a movie. [#permalink]
Show Tags
29 Oct 2014, 09:39
Bunuel wrote: 12bhang wrote: Please help.
If the seats are more than 2N, there is no upper limit.
So, if we use the counting principle, depending on the value of 2N, the number of options available to the first couple could be 100, 1000 or whatever. SUbesquent couples would be limited by where the first couple chose to sit.
In this case, shouldn.t the answer be E? Take a closer look at the second statement: The group will all sit next to one another, starting with the first seat in the row. Hi Can you please explain me meaning of "each couple is indifferent to empty seats next to them"?
_________________
 Sachin
If you like my explanation then please click "Kudos"



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16035

Re: A group consisting of N couples are going to see a movie. [#permalink]
Show Tags
09 Jan 2016, 07:18
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



CEO
Joined: 17 Jul 2014
Posts: 2525
Location: United States (IL)
Concentration: Finance, Economics
GPA: 3.92
WE: General Management (Transportation)

A group consisting of N couples are going to see a movie. [#permalink]
Show Tags
23 Feb 2016, 19:07
bhandariavi wrote: A group consisting of N couples are going to see a movie. The seats in each row of the theater is greater than 2N. If the group decides to all sit in the same row, each couple is indifferent to empty seats next to them, and each couple insists on sitting together, how many seating arrangements are possible?
(1) N = 5
(2) The group will all sit next to one another, starting with the first seat in the row. 1 alone is insufficient..the 5 couples can be arranged in 5!*2!^5 ways (2! because the 2 from the couples can be arranged in 2! ways, and ^5 because 5 pairs). but we are told that there are >2N seats..so this makes us additional problems..what if there are 11 seats? then the total number of ways would be 11!/5!2!...so different numbers... 2 says that the couple will sit starting the first seat from the row..meaning that if there are 11 seats, and there are 5 couples, the couples will sit in the first 10...so the last one is irrelevant, and does not need to be taken into account. this alone is insufficient. 1+2 > we know that there are 5 couples, and that they will take the first seats in the row..so no additional possibilities...total 5!*2!^2



Manager
Joined: 21 Apr 2016
Posts: 189

Re: A group consisting of N couples are going to see a movie. [#permalink]
Show Tags
13 Apr 2017, 17:38
"Each couple is indifferent to empty seats next to them" > doesn't this mean that we need not worry about empty spaces between the couples? In which case, (A) should be the answer.




Re: A group consisting of N couples are going to see a movie.
[#permalink]
13 Apr 2017, 17:38







