Last visit was: 31 Oct 2024, 16:04 It is currently 31 Oct 2024, 16:04
Home
MBA Fair
MBA Fair
GMAT
Messages
Tests
Schools
Reviews
Chat
My Profile
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
Back to Forum
Create Topic
User avatar
yrozenblum
User avatar
Joined: 29 Mar 2020
Last visit: 31 Oct 2024
Posts: 27
Own Kudos:
811
 [53]
Given Kudos: 24
Posts: 27
Kudos: 811
 [53]
A group of 10 friends consists of 5 married couples. How many seating   Updated on: 29 Oct 2023, 12:32
Originally posted by yrozenblum on 29 Oct 2023, 11:03.
Last edited by gmatophobia on 29 Oct 2023, 12:32, edited 1 time in total.
Corrected typographical error
1
Kudos
Add Kudos
52
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

45% (medium)

Question Stats:

66% (01:36) correct 34% (01:43) wrong based on 528 sessions

History

Date
Time
Result
Not Attempted Yet
A group of 10 friends consists of 5 married couples. How many seating arrangements are possible for these 10 friends to be seated in a row of 10 seats with 1 person per seat if each person is seated next to his or her spouse?

A. 45
B. 120
C. 252
D. 3,840
E. 14,400
ShowHide Answer
Official Answer
D
Most Helpful Reply
User avatar
gmatophobia
User avatar
Quant Chat Moderator
Joined: 22 Dec 2016
Last visit: 31 Oct 2024
Posts: 3,131
Own Kudos:
6,398
 [17]
Given Kudos: 1,860
Location: India
Concentration: Strategy, Leadership
Products:
GMAT Club Tests Forum Quiz
Posts: 3,131
Kudos: 6,398
 [17]
A group of 10 friends consists of 5 married couples. How many seating   29 Oct 2023, 11:48
8
Kudos
Add Kudos
9
Bookmarks
Bookmark this Post
yrozenblum
A group of 10 friends consists of 5 married couples. How many seating arrangements are possible for these 10 friends to be seated in a row of 10 seats with 1 person per seat if each person is seated next to his o her spouse?

A. 45
B. 120
C. 252
D. 3,840
E. 14,400

Let's assume that the 5 couples are

  • \(M_1 \quad W_1\)
  • \(M_2 \quad W_2\)
  • \(M_3 \quad W_3\)
  • \(M_4 \quad W_4\)
  • \(M_5 \quad W_5\)

The 5 couples can be placed in 5! ways. Within each group, the couple can interchange their seats. Hence, each couple can be placed in 2 ways. As there are 5 couples, the members in the group can be arranged in \(2^5\) ways

Total = \(5! * 2^5 = 3840\) ways

Option D
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 31 Oct 2024
Posts: 96,533
Own Kudos:
673,098
 [8]
Given Kudos: 87,883
Products:
GMAT Club Tests Forum Quiz
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 96,533
Kudos: 673,098
 [8]
A group of 10 friends consists of 5 married couples. How many seating   14 Apr 2024, 10:20
4
Kudos
Add Kudos
4
Bookmarks
Bookmark this Post
 
gmathero911
Bunuel any similar GMAT Club problems to this one?
­Check the links below:
https://gmatclub.com/forum/a-committee- ... 94068.html (GMAT Prep)
https://gmatclub.com/forum/m06-183707.html (GMAT Club Tests)
https://gmatclub.com/forum/if-there-are ... .html(GMAT Club Tests) 
https://gmatclub.com/forum/given-that-t ... 74964.html
https://gmatclub.com/forum/what-is-the- ... 79901.html
https://gmatclub.com/forum/from-among-a ... 54502.html
https://gmatclub.com/forum/at-a-dance-t ... 45695.html
https://gmatclub.com/forum/at-a-dance-t ... 45694.html
https://gmatclub.com/forum/if-a-committ ... 88772.html
https://gmatclub.com/forum/a-group-of-1 ... 19717.html
https://gmatclub.com/forum/in-how-many- ... 33266.html
https://gmatclub.com/forum/if-4-people- ... 99055.html
https://gmatclub.com/forum/given-that-t ... 58640.html
https://gmatclub.com/forum/a-committee- ... 30617.html

Hope this helps.

 
General Discussion
User avatar
gmathero911
User avatar
Joined: 19 Mar 2023
Last visit: 27 Apr 2024
Posts: 17
Own Kudos:
96
 [1]
Posts: 17
Kudos: 96
 [1]
A group of 10 friends consists of 5 married couples. How many seating   14 Apr 2024, 09:43
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel any similar GMAT Club problems to this one?
User avatar
Yes2GMAT
User avatar
Joined: 30 Dec 2020
Last visit: 29 Jun 2024
Posts: 41
Own Kudos:
9
 [2]
Given Kudos: 176
Posts: 41
Kudos: 9
 [2]
A group of 10 friends consists of 5 married couples. How many seating   06 Jun 2024, 05:41
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
10 * 1, * ,8 * 1, *, 6 *1, *, 4 *1, *, 2 * 1 = 3840

M1 * W1, *, M2 * W2, *, M3 * W3, *, M4 * W4, *, M5 * W5 = 3840

Is this reasoning correct?

With this method, I don't end up multiplying by 2! (to consider when W is chosen first). Hence, the question.
User avatar
babyulikeit
User avatar
Joined: 04 Jul 2024
Last visit: 29 Oct 2024
Posts: 18
Own Kudos:
5
Given Kudos: 32
Location: India
Posts: 18
Kudos: 5
A group of 10 friends consists of 5 married couples. How many seating   06 Sep 2024, 04:18
Kudos
Add Kudos
Bookmarks
Bookmark this Post
gmatophobia
yrozenblum
A group of 10 friends consists of 5 married couples. How many seating arrangements are possible for these 10 friends to be seated in a row of 10 seats with 1 person per seat if each person is seated next to his o her spouse?

A. 45
B. 120
C. 252
D. 3,840
E. 14,400
Let's assume that the 5 couples are


  • \(M_1 \quad W_1\)
  • \(M_2 \quad W_2\)
  • \(M_3 \quad W_3\)
  • \(M_4 \quad W_4\)
  • \(M_5 \quad W_5\)

The 5 couples can be placed in 5! ways. Within each group, the couple can interchange their seats. Hence, each couple can be placed in 2 ways. As there are 5 couples, the members in the group can be arranged in \(2^5\) ways

Total = \(5! * 2^5 = 3840\) ways

Option D
­
gmatophobia
Can you please explain why you multiplied by 2^5 and not 2! ?
Thankyou.
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 31 Oct 2024
Posts: 96,533
Own Kudos:
673,098
 [2]
Given Kudos: 87,883
Products:
GMAT Club Tests Forum Quiz
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 96,533
Kudos: 673,098
 [2]
A group of 10 friends consists of 5 married couples. How many seating   06 Sep 2024, 06:56
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
babyulikeit
gmatophobia
yrozenblum
A group of 10 friends consists of 5 married couples. How many seating arrangements are possible for these 10 friends to be seated in a row of 10 seats with 1 person per seat if each person is seated next to his o her spouse?

A. 45
B. 120
C. 252
D. 3,840
E. 14,400
Let's assume that the 5 couples are




  • \(M_1 \quad W_1\)
  • \(M_2 \quad W_2\)
  • \(M_3 \quad W_3\)
  • \(M_4 \quad W_4\)
  • \(M_5 \quad W_5\)

The 5 couples can be placed in 5! ways. Within each group, the couple can interchange their seats. Hence, each couple can be placed in 2 ways. As there are 5 couples, the members in the group can be arranged in \(2^5\) ways

Total = \(5! * 2^5 = 3840\) ways

Option D
­
gmatophobia
Can you please explain why you multiplied by 2^5 and not 2! ?
Thankyou.
­
We have 5 couples (M1, W1); (M2, W2); (M3, W3); (M4, W4); (M5, W5). These 5 units can be arranged in 5! ways. In each couple, M and W can be arranged in 2 ways. Since there are 5 couples, we get 2 * 2 * 2 * 2 * 2 = 2^5. Therefore, the final answer is 5! * 2^5 = 120 * 32 = 3,840.

Answer: D.­
User avatar
MartyMurray
User avatar
Joined: 11 Aug 2023
Last visit: 31 Oct 2024
Posts: 1,206
Own Kudos:
3,026
Given Kudos: 106
GMAT 1: 800 Q51 V51
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
GMAT 1: 800 Q51 V51
Posts: 1,206
Kudos: 3,026
A group of 10 friends consists of 5 married couples. How many seating   21 Oct 2024, 14:27
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Yes2GMAT
10 * 1, * ,8 * 1, *, 6 *1, *, 4 *1, *, 2 * 1 = 3840

M1 * W1, *, M2 * W2, *, M3 * W3, *, M4 * W4, *, M5 * W5 = 3840

Is this reasoning correct?

With this method, I don't end up multiplying by 2! (to consider when W is chosen first). Hence, the question.
Yes, that approach works without multiplying by 2 because the possibility that W or M is chosen first is accounted for by the 10, 8, 6, 4, and 2.
Moderator:
Bunuel
Math Expert
96533 posts