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

It is currently 21 Nov 2018, 06:59

LIVE NOW!

LBS is Calling R1 Admits - Join Chat Room to Catch the Latest Action


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 in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
  • All GMAT Club Tests are Free and open on November 22nd in celebration of Thanksgiving Day!

     November 22, 2018

     November 22, 2018

     10:00 PM PST

     11:00 PM PST

    Mark your calendars - All GMAT Club Tests are free and open November 22nd to celebrate Thanksgiving Day! Access will be available from 0:01 AM to 11:59 PM, Pacific Time (USA)
  • Key Strategies to Master GMAT SC

     November 24, 2018

     November 24, 2018

     07:00 AM PST

     09:00 AM PST

    Attend this webinar to learn how to leverage Meaning and Logic to solve the most challenging Sentence Correction Questions.

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: 65
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
15
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

57% (02:29) correct 43% (02:23) wrong based on 199 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
Most Helpful Expert Reply
Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8580
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
7
4
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

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

GMAT self-study has never been more personalized or more fun. Try ORION Free!

General Discussion
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50730
Re: In a railway compartment, there are 2 rows of seats facing  [#permalink]

Show Tags

New post 15 Apr 2014, 02:26
2
5
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

Manager
Manager
avatar
B
Joined: 14 Jul 2014
Posts: 177
Location: United States
Schools: Duke '20 (D)
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!?
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50730
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

Director
Director
User avatar
S
Joined: 17 Dec 2012
Posts: 629
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 Holistic Solutions
http://www.sravnatestprep.com

Holistic and Systematic Approach

Intern
Intern
avatar
Joined: 28 Sep 2017
Posts: 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.
Manager
Manager
avatar
G
Joined: 31 Jul 2017
Posts: 187
Location: India
Concentration: General Management, Leadership
GMAT 1: 500 Q47 V15
GPA: 3.4
WE: Information Technology (Computer Software)
Premium Member Reviews Badge 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
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
_________________

If it helps you please press Kudos!

Thank You
Sudhanshu

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 8872
Premium Member
Re: In a railway compartment, there are 2 rows of seats facing  [#permalink]

Show Tags

New post 02 Nov 2018, 16:03
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

GMAT Club Bot
Re: In a railway compartment, there are 2 rows of seats facing &nbs [#permalink] 02 Nov 2018, 16:03
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  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| 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®.