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

It is currently 21 Mar 2019, 11:15

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

How many different ways can 2 students be seated in a row of

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

Hide Tags

 
Manager
Manager
avatar
Joined: 03 Feb 2010
Posts: 60
How many different ways can 2 students be seated in a row of  [#permalink]

Show Tags

New post 17 Feb 2010, 11:27
2
3
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

56% (01:04) correct 44% (01:05) wrong based on 208 sessions

HideShow timer Statistics

How many different ways can 2 students be seated in a row of 4 desks, so that there is always at least one empty desk between the students?

(A) 2
(B) 3
(C) 4
(D) 6
(E) 12
Intern
Intern
avatar
Joined: 14 Nov 2008
Posts: 23
Re: How many different ways can 2 students be seated in a row of  [#permalink]

Show Tags

New post 17 Feb 2010, 11:34
1
3 ways to seat the students:
with two empty seats between
1 empty w/ one student on the left most
1 empty....right most

two students can be interchanged

3x2=6
Manager
Manager
avatar
Joined: 03 Feb 2010
Posts: 60
Re: How many different ways can 2 students be seated in a row of  [#permalink]

Show Tags

New post 17 Feb 2010, 11:47
But that yields the same answer as 4C2? How do you solve use combinations or perm?

That comb above does not take into account the empty seat.
CEO
CEO
User avatar
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2573
Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
Reviews Badge
Re: How many different ways can 2 students be seated in a row of  [#permalink]

Show Tags

New post 17 Feb 2010, 12:04
Take two cases.

case 1... 2 spaces in between that means C1 _ _ C2 or C2_ _ C1

case 2.... 1 space in between.
now consider c1_c2 as one element
Number of ways of arranging these in 4 seats = \(2p2*2!\) = 4

2p2 because we have considered c1_c2 as one element , 2! is rearrangement between c1 and c2

total = 6..whats OA?
_________________

Fight for your dreams :For all those who fear from Verbal- lets give it a fight

Money Saved is the Money Earned :)

Jo Bole So Nihaal , Sat Shri Akaal

:thanks Support GMAT Club by putting a GMAT Club badge on your blog/Facebook :thanks

GMAT Club Premium Membership - big benefits and savings

Gmat test review :
http://gmatclub.com/forum/670-to-710-a-long-journey-without-destination-still-happy-141642.html

Intern
Intern
avatar
Joined: 01 Feb 2010
Posts: 27
Re: How many different ways can 2 students be seated in a row of  [#permalink]

Show Tags

New post 21 Feb 2010, 00:55
2
1
ksharma12 wrote:
But that yields the same answer as 4C2? How do you solve use combinations or perm?

That comb above does not take into account the empty seat.

Here order is important, therefore, we'll use Perm.

All the possible ways in which 2 stud can be seated on 4 seats = 4P2.
Suppose, two students are always seated together. Then we'll treat them as 1 stud & the seats left to be filled are 3. Therefore no. of ways in which 2 stud are always seated together = 3P2.

Now, the no. of ways in which 2 students have a gap in between = total no. of ways - no. of ways in which students are seated together = 4P2-3P2 = 12-6 = 6
Manager
Manager
avatar
Joined: 01 Feb 2010
Posts: 226
Re: How many different ways can 2 students be seated in a row of  [#permalink]

Show Tags

New post 24 Feb 2010, 01:18
ksharma12 wrote:
How many different ways can 2 students be seated
in a row of 4 desks, so that there is always at
least one empty desk between the students?

(A) 2
(B) 3
(C) 4
(D) 6
(E) 12
Easy Question I know. Explanation please?


Possible patterns = 1x2x, 1xx2, x1x2, 2x1x, x2x1, 2xx1 = 6 hence D

Whats the OA
Intern
Intern
avatar
Joined: 13 Aug 2013
Posts: 21
Re: How many different ways can 2 students be seated in a row of  [#permalink]

Show Tags

New post 13 Jul 2014, 01:31
1
Total cases : 12 ( student one has 4 options and student two has three options, 4x3=12)
Non-favourable cases : 6 (when two students sit together. students in desk 1 and desk 2 , in desk 2 and desk 3, in desk 3 and desk 4) for each of these cases there are two possibilities because the positions can be interchanged. hence 2x3=6.

SO favourable cases : 12-6=6.
Manager
Manager
User avatar
Joined: 10 Mar 2013
Posts: 189
GMAT 1: 620 Q44 V31
GMAT 2: 690 Q47 V37
GMAT 3: 610 Q47 V28
GMAT 4: 700 Q50 V34
GMAT 5: 700 Q49 V36
GMAT 6: 690 Q48 V35
GMAT 7: 750 Q49 V42
GMAT 8: 730 Q50 V39
How many different ways can 2 students be seated in a row of  [#permalink]

Show Tags

New post 26 Nov 2015, 10:49
It is important to see that the empty desks are not distinct (I missed this the first time, because I considered them to be)
We have "4" students (2 normal students {\(A\),\(B\)} and 2 students {\(E_1\),\(E_2\)} that we can consider empty desks) and 4 places.
Total = \(\frac{4!}{2!}\) since \(AE_1E_2B=AE_2E_1B\)
Cases in which the two students are together {{\(A\),\(B\)}, \(E_1\), \(E_2\)} = 3!*2!/2! since \(ABE_1E_2\) = \(ABE_2E_1\)
Total - together = 12 - 6 = 6
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 13768
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: How many different ways can 2 students be seated in a row of  [#permalink]

Show Tags

New post 26 Nov 2015, 16:44
Hi All,

Since the answers to this question are all small, and the question has a strong 'visual' component to it, we can 'brute force' the answer by drawing some pictures.

If we call the two students 'X' and 'Y', we have the following possibilities:

X _ Y _
Y _ X _

X _ _ Y
Y _ _ X

_ X _ Y
_ Y _ X

Total options: 6

Final Answer:

GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free
  Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 10166
Premium Member
Re: How many different ways can 2 students be seated in a row of  [#permalink]

Show Tags

New post 18 Feb 2019, 04:05
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: How many different ways can 2 students be seated in a row of   [#permalink] 18 Feb 2019, 04:05
Display posts from previous: Sort by

How many different ways can 2 students be seated in a row of

  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®.