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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 350,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

A family consisting of one mother, one father, two daughters [#permalink]
27 Apr 2012, 02:57

1

This post received KUDOS

4

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

55% (hard)

Question Stats:

66% (01:57) correct
34% (01:20) wrong based on 185 sessions

A family consisting of one mother, one father, two daughters and a son is taking a road trip in a sedan. The sedan has two front seats and three back seats. If one of the parents must drive and the two daughters refuse to sit next to each other, how many possible seating arrangements are there?

A family consisting of one mother, one father, two daughters and a son is taking a road trip in a sedan. The sedan has two front seats and three back seats. If one of the parents must drive and the two daughters refuse to sit next to each other, how many possible seating arrangements are there? A. 28 B. 32 C. 48 D. 60 E. 120

Approach #1:

Sisters can sit separately in two ways:

1. one of them is on the front seat (2 ways). Others (including second sister) can be arranged in: 2 (drivers seat)*3! (arrangements of three on the back seat)=12 ways. Total for this case: 2*12=24

Or

2. both by the window on the back seat (2 ways). Others can be arranged in: 2 (drivers seat)*2 (front seat)*1(one left to sit between the sisters on the back seat)=4 ways. Total for this case: 2*4=8.

Total=24+8=32.

Approach #2:

Total # of arrangements: Drivers seat: 2 (either mother or father); Front seat: 4 (any of 4 family members left); Back seat: 3! (arranging other 3 family members on the back seat); So. total # of arrangements is 2*4*3!=48.

# of arrangements with sisters sitting together: Sisters can sit together only on the back seat either by the left window or by the right window - 2, and either {S1,S2} or {S2,S1} - 2 --> 2*2=4; Drivers seat: 2 (either mother or father); Front seat: 2 (5 - 2 sisters on back seat - 1 driver = 2); Back seat with sisters: 1 (the last family member left); So, # of arrangements with sisters sitting together is 4*2*2*1=16.

Re: A family consisting of one mother, one father, two daughters [#permalink]
27 Apr 2012, 09:30

2

This post received KUDOS

pratikbais wrote:

A family consisting of one mother, one father, two daughters and a son is taking a road trip in a sedan. The sedan has two front seats and three back seats. If one of the parents must drive and the two daughters refuse to sit next to each other, how many possible seating arrangements are there?

A. 28 B. 32 C. 48 D. 60 E. 120

Steps to solve this problem - People - 1M, 1F, 1S, 2D (D1,D2) 1. Choose a parent to drive the sedan. 2. Find the ways to seat the daughters. 3. Place the remaining 3 family members. 4. Finally multiply results from steps 1, 2 and 3.

1. Ways to choose a parent to drive = 2 (One person seated, total remaining = 4). 2. Arrangement in which daughters sit separate = Total Arrangements of 4 people - Arrangements with D1 and D2 glued together.

-> 4! - 4*2*1

4*2*1 - the pair of daughters can take 2 out of 3 consecutive spots at the back seat. Also they can interchange seats D1D2 and D2D1 are different arrangements. So total 4. Remaining two people sit in 2*1 ways.

Re: A family consisting of one mother, one father, two daughters [#permalink]
28 Dec 2012, 19:05

1

This post was BOOKMARKED

pratikbais wrote:

A family consisting of one mother, one father, two daughters and a son is taking a road trip in a sedan. The sedan has two front seats and three back seats. If one of the parents must drive and the two daughters refuse to sit next to each other, how many possible seating arrangements are there?

A. 28 B. 32 C. 48 D. 60 E. 120

Case 1: Both daughters in the back seat but seated separately Case 2: One daughter in front seat and the other in the middle of the back seat Case 3: One daughter in front seat and the other in the right back seat Case 4: One daugther in front seat and the other in the left back seat

That's 4 positions and two daughters are interchangeable. Thus, 8.

There are 2 ways to select a parent and 2 ways to seat the son and another parent.

Re: A family consisting of one mother, one father, two daughters [#permalink]
24 Jul 2014, 21:21

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. _________________

Re: A family consisting of one mother, one father, two daughters [#permalink]
26 Jul 2014, 09:23

1

This post was BOOKMARKED

Could someone tell me is my approach is correct?

1) Total of arrangement in the driver seat : 2 (mother or father)

2) Total arrangement of the four others : 4!

3) Total ways with the 2 daughters next to each other : 4 (left window D1-D2 and D2-D1, right window D1-D2 and D2-D1) *2 (we have to place the mother or father that is not driving)

Re: A family consisting of one mother, one father, two daughters [#permalink]
26 Jul 2014, 09:53

Expert's post

oss198 wrote:

Could someone tell me is my approach is correct?

1) Total of arrangement in the driver seat : 2 (mother or father)

2) Total arrangement of the four others : 4!

3) Total ways with the 2 daughters next to each other : 4 (left window D1-D2 and D2-D1, right window D1-D2 and D2-D1) *2 (we have to place the mother or father that is not driving)

Re: A family consisting of one mother, one father, two daughters [#permalink]
16 Sep 2014, 02:25

Bunuel wrote:

A family consisting of one mother, one father, two daughters and a son is taking a road trip in a sedan. The sedan has two front seats and three back seats. If one of the parents must drive and the two daughters refuse to sit next to each other, how many possible seating arrangements are there? A. 28 B. 32 C. 48 D. 60 E. 120

Approach #1:

Sisters can sit separately in two ways:

1. one of them is on the front seat (2 ways). Others (including second sister) can be arranged in: 2 (drivers seat)*3! (arrangements of three on the back seat)=12 ways. Total for this case: 2*12=24

Or

2. both by the window on the back seat (2 ways). Others can be arranged in: 2 (drivers seat)*2 (front seat)*1(one left to sit between the sisters on the back seat)=4 ways. Total for this case: 2*4=8.

Total=24+8=32.

Approach #2:

Total # of arrangements: Drivers seat: 2 (either mother or father); Front seat: 4 (any of 4 family members left); Back seat: 3! (arranging other 3 family members on the back seat); So. total # of arrangements is 2*4*3!=48.

# of arrangements with sisters sitting together: Sisters can sit together only on the back seat either by the left window or by the right window - 2, and either {S1,S2} or {S2,S1} - 2 --> 2*2=4; Drivers seat: 2 (either mother or father); Front seat: 2 (5 - 2 sisters on back seat - 1 driver = 2); Back seat with sisters: 1 (the last family member left); So, # of arrangements with sisters sitting together is 4*2*2*1=16.

48-16=32.

Answer: B.

Sorry Bunuel, but i didnt get the above in red. Why the 4*2*2*1 _________________

If you found this post useful for your prep, click 'Kudos'

Re: A family consisting of one mother, one father, two daughters [#permalink]
16 Sep 2014, 12:34

1

This post received KUDOS

Expert's post

alphonsa wrote:

Bunuel wrote:

A family consisting of one mother, one father, two daughters and a son is taking a road trip in a sedan. The sedan has two front seats and three back seats. If one of the parents must drive and the two daughters refuse to sit next to each other, how many possible seating arrangements are there? A. 28 B. 32 C. 48 D. 60 E. 120

Approach #1:

Sisters can sit separately in two ways:

1. one of them is on the front seat (2 ways). Others (including second sister) can be arranged in: 2 (drivers seat)*3! (arrangements of three on the back seat)=12 ways. Total for this case: 2*12=24

Or

2. both by the window on the back seat (2 ways). Others can be arranged in: 2 (drivers seat)*2 (front seat)*1(one left to sit between the sisters on the back seat)=4 ways. Total for this case: 2*4=8.

Total=24+8=32.

Approach #2:

Total # of arrangements: Drivers seat: 2 (either mother or father); Front seat: 4 (any of 4 family members left); Back seat: 3! (arranging other 3 family members on the back seat); So. total # of arrangements is 2*4*3!=48.

# of arrangements with sisters sitting together: Sisters can sit together only on the back seat either by the left window or by the right window - 2, and either {S1,S2} or {S2,S1} - 2 --> 2*2=4; Drivers seat: 2 (either mother or father); Front seat: 2 (5 - 2 sisters on back seat - 1 driver = 2); Back seat with sisters: 1 (the last family member left); So, # of arrangements with sisters sitting together is 4*2*2*1=16.

48-16=32.

Answer: B.

Sorry Bunuel, but i didnt get the above in red. Why the 4*2*2*1

4 ways to sit sisters together; 2 ways to fill drivers seat (mother or father); 2 ways to fill front seat (3 people are already distributed, so 2 are left); 1 way to fill the remaining back seat.

Hey, Last week I started a few new things in my life. That includes shifting from daily targets to weekly targets, 45 minutes of exercise including 15 minutes of yoga, making...

This week went in reviewing all the topics that I have covered in my previous study session. I reviewed all the notes that I have made and started reviewing the Quant...

I started running as a cross country team member since highshcool and what’s really awesome about running is that...you never get bored of it! I participated in...