[GMAT math practice question]
Alice, Bob, Cindy, Darren, Eddie, Fabian sit on six chairs around a large round table. Alice must sit opposite Bob and Cindy must sit opposite Darren. How many seating arrangements are possible?
A. 6
B. 8
C. 24
D. 120
E. 720
Alice, Bob, Cindy, Darren, Eddie, Fabian sit on six chairs a
This topic has expert replies
- Max@Math Revolution
- Elite Legendary Member
- Posts: 3991
- Joined: Fri Jul 24, 2015 2:28 am
- Location: Las Vegas, USA
- Thanked: 19 times
- Followed by:37 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
Math Revolution
The World's Most "Complete" GMAT Math Course!
Score an excellent Q49-51 just like 70% of our students.
[Free] Full on-demand course (7 days) - 100 hours of video lessons, 490 lesson topics, and 2,000 questions.
[Course] Starting $79 for on-demand and $60 for tutoring per hour and $390 only for Live Online.
Email to : [email protected]
- GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
To count circular arrangements:Max@Math Revolution wrote:[GMAT math practice question]
Alice, Bob, Cindy, Darren, Eddie, Fabian sit on six chairs around a large round table. Alice must sit opposite Bob and Cindy must sit opposite Darren. How many seating arrangements are possible?
A. 6
B. 8
C. 24
D. 120
E. 720
1. Place someone in the circle
2. Count the number of ways to arrange the REMAINING people
Once Alice has been placed in the circle:
Number of options for Bob = 1. (Must be in the seat opposite Alice)
Number of options for Cindy = 4. (Any of the 4 remaining seats)
Number of options for Darren = 1. (Must be in the seat opposite Cindy)
Number of options for Eddie =2. (Either of the 2 remaining seats)
Number of options for Fabian = 1. (The last remaining seat)
To combine these options, we multiply:
1*4*1*2*1 = 8
The correct answer is B.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
- Max@Math Revolution
- Elite Legendary Member
- Posts: 3991
- Joined: Fri Jul 24, 2015 2:28 am
- Location: Las Vegas, USA
- Thanked: 19 times
- Followed by:37 members
=>
Note: Because the table is round, Alice's choice of chair does not change the number of possible arrangements.
Once Alice is seated, Bob's position is determined. Cindy has 4 remaining possible seats. Cindy's choice determines Darren's position. Eddie then has 2 remaining possible seats, and Fabian must sit in the remaining chair.
Thus, the number of possible arrangements is 4*2 = 8.
Therefore, B is the answer.
Answer: B
Note: Because the table is round, Alice's choice of chair does not change the number of possible arrangements.
Once Alice is seated, Bob's position is determined. Cindy has 4 remaining possible seats. Cindy's choice determines Darren's position. Eddie then has 2 remaining possible seats, and Fabian must sit in the remaining chair.
Thus, the number of possible arrangements is 4*2 = 8.
Therefore, B is the answer.
Answer: B
Math Revolution
The World's Most "Complete" GMAT Math Course!
Score an excellent Q49-51 just like 70% of our students.
[Free] Full on-demand course (7 days) - 100 hours of video lessons, 490 lesson topics, and 2,000 questions.
[Course] Starting $79 for on-demand and $60 for tutoring per hour and $390 only for Live Online.
Email to : [email protected]