• 7 CATs FREE!
    If you earn 100 Forum Points

    Engage in the Beat The GMAT forums to earn
    100 points for $49 worth of Veritas practice GMATs FREE

    Veritas Prep
    VERITAS PRACTICE GMAT EXAMS
    Earn 10 Points Per Post
    Earn 10 Points Per Thanks
    Earn 10 Points Per Upvote
    REDEEM NOW

In how many ways four men, two women and one child can sit a

This topic has 2 expert replies and 1 member reply

In how many ways four men, two women and one child can sit a

Post

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Difficult



In how many ways four men, two women and one child can sit at a circular 7-seats table if the child is the only person to be seated between the two women?

(A) 24
(B) 36
(C) 48
(D) 96
(E) 240

Answer: __(C)_____
Difficulty Level: 650 - 700
Source: www.GMATH.net

_________________
Fabio Skilnik :: https://GMATH.net (Math for the GMAT) or https://GMATH.com.br (Portuguese version)
Course release PROMO : finish our test drive till 30/Dec with (at least) 50 correct answers out of 92 (12-questions Mock included) to gain a 50% discount!

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post
fskilnik wrote:
In how many ways four men, two women and one child can sit at a circular 7-seats table if the child is the only person to be seated between the two women?

(A) 24
(B) 36
(C) 48
(D) 96
(E) 240
Once the child has been placed at the table:
Number of ways to arrange the 2 women in the 2 seats adjacent to the child = 2! = 2.
Number of ways to arrange the 4 men in the remaining 4 seats = 4! = 24.
To combine these options, we multiply:
2*24 = 48.

The correct answer is C.

_________________
Mitch Hunt
Private Tutor for the GMAT and GRE
GMATGuruNY@gmail.com

If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon.

Available for tutoring in NYC and long-distance.
For more information, please email me at GMATGuruNY@gmail.com.
Student Review #1
Student Review #2
Student Review #3



Last edited by GMATGuruNY on Mon Sep 24, 2018 3:08 pm; edited 1 time in total

  • +1 Upvote Post
  • Quote
  • Flag
Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now.
Post
fskilnik wrote:
In how many ways four men, two women and one child can sit at a circular 7-seats table if the child is the only person to be seated between the two women?

(A) 24
(B) 36
(C) 48
(D) 96
(E) 240

Source: www.GMATH.net
Thank you for the nice contribution, Mitch!
(I believe this is the most direct - hence the better - argument, by the way.)

Alternate solution:

Let´s imagine a linear version (=row), but "connecting the first seat to the last one" (so that after the last seat we have again the first one).



There are 7 seats in which the child could be seated.

Once (any) one of the 7 seats is chosen, there are 2 ways to seat the two women.
(If the child is in the 7th seat, W1 will be in the 6th, W2 in the 1st... or vice-versa!)

Once the child and the two women are seated, there are 4! ways of seating the men.

Using the Multiplicative Principle, we have 7*2*4! ways of seating these people in the linear version.

The "linear to circular migration" is done dividing 7*2*4! by the number of objects to be circularized (7),
checking the "connection" created earlier do not give rise to unwanted configurations: it does not! (*)

Hence:
\[? = \frac{{7 \cdot 2 \cdot 4!}}{7} = 48\]

(*) Typical problem: when A and B cannot stay next to each other, in the linear version you cannot allow one of them to be in
the first place and the other in the last place, because when the connection is established they would violate the restriction!

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

_________________
Fabio Skilnik :: https://GMATH.net (Math for the GMAT) or https://GMATH.com.br (Portuguese version)
Course release PROMO : finish our test drive till 30/Dec with (at least) 50 correct answers out of 92 (12-questions Mock included) to gain a 50% discount!



Last edited by fskilnik@GMATH on Thu Sep 27, 2018 3:36 pm; edited 2 times in total

  • +1 Upvote Post
  • Quote
  • Flag
Post
Let women be numbered as w1 and w2 and child be as c
The arrangement can be done as w1cw2 or w2cw1 I.e. 2 ways

Now group the women children as one so in addition to 4 other men, there are 5 entities to be arranged in a circle which can be done in (n-1)! Ways = (5-1)!= 4!= 24 ways

So total ways = 2*24 = 48 ways

  • +1 Upvote Post
  • Quote
  • Flag
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • The Princeton Review
    FREE GMAT Exam
    Know how you'd score today for $0

    Available with Beat the GMAT members only code

    MORE DETAILS
    The Princeton Review
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep

Top First Responders*

1 Brent@GMATPrepNow 65 first replies
2 fskilnik@GMATH 55 first replies
3 Jay@ManhattanReview 44 first replies
4 GMATGuruNY 34 first replies
5 Rich.C@EMPOWERgma... 32 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

Most Active Experts

1 image description fskilnik@GMATH

GMATH Teacher

135 posts
2 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

103 posts
3 image description Max@Math Revolution

Math Revolution

90 posts
4 image description Jay@ManhattanReview

Manhattan Review

82 posts
5 image description Rich.C@EMPOWERgma...

EMPOWERgmat

80 posts
See More Top Beat The GMAT Experts