It is currently 21 Jan 2018, 12:18

Close

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
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.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

In a railway compartment, there are 2 rows of seats facing

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Current Student
User avatar
Joined: 27 Jan 2013
Posts: 76

Kudos [?]: 30 [0], given: 4

Concentration: Marketing, Strategy
GMAT 1: 730 Q50 V38
GPA: 3
WE: Engineering (Telecommunications)
In a railway compartment, there are 2 rows of seats facing [#permalink]

Show Tags

New post 15 Apr 2014, 02:15
10
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

59% (02:22) correct 41% (02:16) wrong based on 165 sessions

HideShow timer Statistics

In a railway compartment, there are 2 rows of seats facing each other with accommodation for 5 in each, 4 wish to sit facing forward and 3 facing towards the rear while 3 others are indifferent. In how many ways can the 10 passengers be seated?


A.172000


B.12600


C.45920


D.43200
[Reveal] Spoiler: OA

Kudos [?]: 30 [0], given: 4

Expert Post
2 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 43348

Kudos [?]: 139702 [2], given: 12794

Re: In a railway compartment, there are 2 rows of seats facing [#permalink]

Show Tags

New post 15 Apr 2014, 02:26
2
This post received
KUDOS
Expert's post
5
This post was
BOOKMARKED
suryav wrote:
In a railway compartment, there are 2 rows of seats facing each other with accommodation for 5 in each, 4 wish to sit facing forward and 3 facing towards the rear while 3 others are indifferent. In how many ways can the 10 passengers be seated?


A.172000


B.12600


C.45920


D.43200


A --> E
B --> F
C --> G
D --> X
X --> X

The total number of arrangements = \(5!*5!*C^1_3=43,200\), where 5! is the number of ways to arrange 5 people facing forward, 5! is the number of ways to arrange 5 people facing backward, and \(C^1_3\) is the number of ways to choose 1 out of 3 indifferent who will face forward (the remaining 2 will face backward).

Answer: D.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 139702 [2], given: 12794

Manager
Manager
avatar
B
Joined: 14 Jul 2014
Posts: 191

Kudos [?]: 19 [0], given: 110

Location: United States
GMAT 1: 600 Q48 V27
GMAT 2: 720 Q50 V37
GPA: 3.2
Reviews Badge
In a railway compartment, there are 2 rows of seats facing [#permalink]

Show Tags

New post 25 Oct 2015, 07:50
I can understand the last 3! (for the 3 who are indifferent) but should not we do factorial for 4 facing front and 3 facing rear?

How do we get 5! * 5!?

Kudos [?]: 19 [0], given: 110

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 43348

Kudos [?]: 139702 [0], given: 12794

In a railway compartment, there are 2 rows of seats facing [#permalink]

Show Tags

New post 25 Oct 2015, 07:58
dina98 wrote:
I can understand the last 3! (for the 3 who are indifferent) but should not we do factorial for 4 facing front and 3 facing rear?

How do we get 5! * 5!?


In each row the number of arrangements is 5! because there are 5 seats. Hence, 5!*5!.

Next, there are 3 people which does not care where they sit. \(C^1_3=3\) is the number of ways to choose which one of them will sit with 4 wishing to sit facing forward and the remaining 2 will automatically be placed with 3 wishing to sit facing towards the rear.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 139702 [0], given: 12794

Expert Post
6 KUDOS received
Veritas Prep GMAT Instructor
User avatar
G
Joined: 16 Oct 2010
Posts: 7869

Kudos [?]: 18503 [6], given: 237

Location: Pune, India
Re: In a railway compartment, there are 2 rows of seats facing [#permalink]

Show Tags

New post 25 Oct 2015, 21:13
6
This post received
KUDOS
Expert's post
3
This post was
BOOKMARKED
suryav wrote:
In a railway compartment, there are 2 rows of seats facing each other with accommodation for 5 in each, 4 wish to sit facing forward and 3 facing towards the rear while 3 others are indifferent. In how many ways can the 10 passengers be seated?


A.172000


B.12600


C.45920


D.43200


Here is another way to think about it - each seat is distinct. 5 face forward and 5 face back.
Start with the 4 people who want to face forward - for the first one, there are 5 options, for next one, 4 options and so on till we get 5*4*3*2.
Next, go on to 3 people who want to face back - for the first one, there are 5 options, for the next one, 4 options and so on till we get 5*4*3.
Now, we have 3 seats leftover and 3 indifferent people who can be arranged in 3*2*1 ways.
All in all, we can arrange 10 people in 5*4*3*2*5*4*3*3*2*1 = 14400 * 3 = 43200

Answer (D)
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

Kudos [?]: 18503 [6], given: 237

Expert Post
Director
Director
User avatar
B
Joined: 17 Dec 2012
Posts: 624

Kudos [?]: 557 [0], given: 16

Location: India
In a railway compartment, there are 2 rows of seats facing [#permalink]

Show Tags

New post 26 Oct 2015, 00:30
This is permutation since order needs to be considered
4 persons have a choice of 5 seats (5P4), again 3 persons have a choice of 5 seats (5P3)and the remaining 3 persons in the remaining 3 seats(3!).
Total number of arrangements is 5P4*5P3*3!=43,200
_________________

Srinivasan Vaidyaraman
Sravna
http://www.sravnatestprep.com

Premium Material
Standardized Approaches

Kudos [?]: 557 [0], given: 16

Intern
Intern
avatar
Joined: 28 Sep 2017
Posts: 4

Kudos [?]: 0 [0], given: 2

Re: In a railway compartment, there are 2 rows of seats facing [#permalink]

Show Tags

New post 15 Oct 2017, 02:00
Can someone help me solve this in slot method. I tried but was not successful.

I considered FFFFRRRIII , F being facing forward, R being facing rear and I being indifferent. this can be arranged in 10!/4!3!3!. What is wrong in my approach.

Thanks.

Kudos [?]: 0 [0], given: 2

Intern
Intern
avatar
B
Joined: 31 Jul 2017
Posts: 11

Kudos [?]: 7 [0], given: 164

CAT Tests
Re: In a railway compartment, there are 2 rows of seats facing [#permalink]

Show Tags

New post 21 Oct 2017, 01:09
1
This post was
BOOKMARKED
Hi,
I think you considered all in one row. But question clearly states - there are 2 rows of seats facing each other with accommodation for 5 in each.

F=>F1 F2 F3 F4 I1
R=>R1 R2 R3 I2 I3

Lets select and arrange F row for (F1 to F4)- > 5C4*4! .= 5*4! = 5! = 120
Lets select and arrange R row for (R1 to R3)- > 5C3*3!.=10 * 6 = 60
Now remaining 3 indifferent can be arranged in 3! = 6 ways.

Total = 120*60*6 = 43200

Ans : - D

Kudos [?]: 7 [0], given: 164

Re: In a railway compartment, there are 2 rows of seats facing   [#permalink] 21 Oct 2017, 01:09
Display posts from previous: Sort by

In a railway compartment, there are 2 rows of seats facing

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.