Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 31 Aug 2016, 19:53

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 June
Open Detailed Calendar

A family consisting of one mother, one father, two daughters

Author Message
TAGS:

Hide Tags

Intern
Joined: 01 Sep 2008
Posts: 3
Followers: 0

Kudos [?]: 3 [0], given: 0

A family consisting of one mother, one father, two daughters [#permalink]

Show Tags

01 Sep 2008, 22:30
3
This post was
BOOKMARKED
00:00

Difficulty:

65% (hard)

Question Stats:

56% (01:38) correct 44% (01:05) wrong based on 91 sessions

HideShow timer Statistics

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

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-family-consisting-of-one-mother-one-father-two-daughters-131430.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 19 Sep 2013, 09:27, edited 1 time in total.
Intern
Joined: 03 Mar 2008
Posts: 47
Followers: 1

Kudos [?]: 7 [1] , given: 0

Show Tags

01 Sep 2008, 22:46
1
KUDOS
gmatkudi 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?
28
32
48
60
120

IMO 32

Scenario 1:
Mom driving and dad in front.
2 seating arrangements

Scenario 2:
Mom driving and son in front
2 seating arrangements possible

Scenario 3:
Mom driving and one of the sisters in the front.
Sister 2 has (3*2*1 = 6) possible arrangements to sit.

Scenario 4:
Mom driving and the other sister in front'
Same logic as scenario 3....6 possible arrangements

Total scenarios for mom driving = 2+2+6+6 =16
Hence total possible scenarios = 16*2 = 32
Current Student
Joined: 11 May 2008
Posts: 555
Followers: 8

Kudos [?]: 143 [0], given: 0

Show Tags

01 Sep 2008, 23:21
yes, i also got the same thing..
Senior Manager
Joined: 29 Mar 2008
Posts: 348
Followers: 4

Kudos [?]: 69 [0], given: 0

Show Tags

01 Sep 2008, 23:26
gmatkudi 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?
28
32
48
60
120

Total # ways possible (with only one constraint of one parent sitting in front)
= 4! *2 = 48

# ways, when both the daughters are sitting together: (P1-Parent1, P2- Parent2, S-Son, D- Daughter)
P1 S D D P2 -> 2 ways (for daughter) + 2 ways (when P1 is swapped with P2)= 4 ways
P1 S P2 D D -> 2 ways (for daughter) + 2 ways (when P1 is swapped with P2)= 4 ways
P1 P2 D D S -> 2 ways (for daughter) + 2 ways (when P1 is swapped with P2)= 4 ways
P1 P2 S D D -> 2 ways (for daughter) + 2 ways (when P1 is swapped with P2)= 4 ways
Total = 16 ways.

Number of ways both the daughters NOT sit near each other = 48-16= 32

WHat is OA?
_________________

To find what you seek in the road of life, the best proverb of all is that which says:
"Leave no stone unturned."
-Edward Bulwer Lytton

SVP
Joined: 07 Nov 2007
Posts: 1820
Location: New York
Followers: 31

Kudos [?]: 780 [0], given: 5

Show Tags

02 Sep 2008, 12:20
gmatkudi 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?
28
32
48
60
120

PX
DDX

= Total No of ways - two daughters sit together
= 2*4! - 2 (choose 1 Parent for Driver seat)* 2(Daughters can be arranged themselves) * 2 (DD and X (backseat) arranged in themselves) * 2( X and X can be aranged in two ways)
=48 -2*2*2*2
=32
_________________

Smiling wins more friends than frowning

Senior Manager
Joined: 08 Apr 2012
Posts: 464
Followers: 1

Kudos [?]: 41 [0], given: 58

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

Show Tags

19 Sep 2013, 07:44
I tried a different solution but was unsuccessfull.
Can anyone see where I went wrong?

I tried it so:
Number of all possible seating arrangements (2*4!) = 48
Number of seating arrangements where girls seat together and one parent drives:
2*2*3!.....

and then subtracting the two.

Can anyone see where I went wrong?
Math Expert
Joined: 02 Sep 2009
Posts: 34527
Followers: 6313

Kudos [?]: 80121 [4] , given: 10027

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

Show Tags

19 Sep 2013, 09:28
4
KUDOS
Expert's post
1
This post was
BOOKMARKED
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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-family-consisting-of-one-mother-one-father-two-daughters-131430.html
_________________
Re: A family consisting of one mother, one father, two daughters   [#permalink] 19 Sep 2013, 09:28
Similar topics Replies Last post
Similar
Topics:
1 A family with 1 mother, 1 father, and 3 children sit in a car with 2 2 30 May 2016, 13:33
2 A family with 1 mother, 1 father, and 3 children sit in a car with 2 4 30 May 2016, 13:20
5 The Coen family consists of a father, a mother, two children 6 30 May 2012, 22:13
46 A family consisting of one mother, one father, two daughters 9 27 Apr 2012, 03:57
10 A family consisting of one mother, one father, two daughters 18 09 Mar 2008, 13:33
Display posts from previous: Sort by