GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 15 Dec 2018, 11:30

### 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

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

## Events & Promotions

###### Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
• ### FREE Quant Workshop by e-GMAT!

December 16, 2018

December 16, 2018

07:00 AM PST

09:00 AM PST

Get personalized insights on how to achieve your Target Quant Score.

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

Author Message
TAGS:

### Hide Tags

GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 544
In how many ways four men, two women and one child can sit at a circul  [#permalink]

### Show Tags

24 Sep 2018, 12:26
00:00

Difficulty:

55% (hard)

Question Stats:

50% (01:47) correct 50% (01:22) wrong based on 62 sessions

### HideShow timer Statistics

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: http://www.GMATH.net

_________________

Fabio Skilnik :: https://GMATH.net (Math for the GMAT) or 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!

Intern
Joined: 09 Jun 2016
Posts: 10
GMAT 1: 710 Q48 V39
GMAT 2: 730 Q49 V39
Re: In how many ways four men, two women and one child can sit at a circul  [#permalink]

### Show Tags

24 Sep 2018, 12:54
Let women be numbered as w1 and w2 and child be as c
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

Posted from my mobile device
GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 544
In how many ways four men, two women and one child can sit at a circul  [#permalink]

### Show Tags

24 Sep 2018, 14:27
1
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: http://www.GMATH.net

$$?\,\,\,:\,\,\,\,\# \,\,{\text{circular}}\,\,{\text{permutations}}\,\,{\text{with}}\,\,{\text{restrictions}}$$

Let the child be placed in any seat.
Once this is done, there are 2 ways of placing the women (W1 to-the-right of the child, W2 to-the-left of the child... and vice-versa).
Once the child and the women are seated, there are 4! ways of placing the men.

From the Multiplicative Principle:

$${\text{?}}\,\,\, = \,\,\,2 \cdot 4!\,\,\, = \,\,48$$

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

Regards,
Fabio.
_________________

Fabio Skilnik :: https://GMATH.net (Math for the GMAT) or 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!

GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 544
In how many ways four men, two women and one child can sit at a circul  [#permalink]

### Show Tags

24 Sep 2018, 14:32
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: http://www.GMATH.net

$$?\,\,\,:\,\,\,\,\# \,\,{\text{circular}}\,\,{\text{permutations}}\,\,{\text{with}}\,\,{\text{restrictions}}$$

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 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!

In how many ways four men, two women and one child can sit at a circul &nbs [#permalink] 24 Sep 2018, 14:32
Display posts from previous: Sort by