It is currently 25 Feb 2018, 11:49

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

M05-27

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

Hide Tags

Expert Post
2 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 43916
M05-27 [#permalink]

Show Tags

New post 15 Sep 2014, 23:26
2
This post received
KUDOS
Expert's post
13
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

68% (00:37) correct 32% (00:59) wrong based on 234 sessions

HideShow timer Statistics

Carly has three movies that she can watch during the weekend: an action movie, a comedy, or a drama. However, she wants to watch the same drama movie three times, an action movie once and a comedy movie also once. In how many different ways can she arrange these five screenings?

A. 6
B. 20
C. 24
D. 60
E. 120
[Reveal] Spoiler: OA

_________________

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

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 43916
Re M05-27 [#permalink]

Show Tags

New post 15 Sep 2014, 23:26
Expert's post
5
This post was
BOOKMARKED
Official Solution:

Carly has three movies that she can watch during the weekend: an action movie, a comedy, or a drama. However, she wants to watch the same drama movie three times, an action movie once and a comedy movie also once. In how many different ways can she arrange these five screenings?

A. 6
B. 20
C. 24
D. 60
E. 120


The number of different ways Carly can watch Drama, Drama, Drama, Action, Comedy (DDDAC) is basically the number of arrangements of 5 letters DDDAC out of which 3 D's are identical, so it's \(\frac{5!}{3!}=20\).


Answer: B
_________________

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

Current Student
User avatar
Joined: 06 Mar 2014
Posts: 267
Location: India
GMAT Date: 04-30-2015
Reviews Badge
Re: M05-27 [#permalink]

Show Tags

New post 16 Sep 2014, 11:19
Bunuel wrote:
Official Solution:

Carly has three movies that she can watch during the weekend: an action movie, a comedy, or a drama. However, she wants to watch the same drama movie three times, an action movie once and a comedy movie also once. In how many different ways can she arrange these five screenings?

A. 6
B. 20
C. 24
D. 60
E. 120


The number of different ways Carly can watch Drama, Drama, Drama, Action, Comedy (DDDAC) is basically the number of arrangements of 5 letters DDDAC out of which 3 D's are identical, so it's \(\frac{5!}{3!}=20\).


Answer: B


Hi Bunuel,

The above explanation is perfect. Thank you.
However, if the question asks with respect to DDDAC, how many ways that 3Ds are NOT Together then how exactly should one approach?

I think: Total ways possible - when the 3Ds are together.
ie. 5!/3! - ?
Expert Post
2 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 43916
Re: M05-27 [#permalink]

Show Tags

New post 16 Sep 2014, 13:39
2
This post received
KUDOS
Expert's post
2
This post was
BOOKMARKED
earnit wrote:
Bunuel wrote:
Official Solution:

Carly has three movies that she can watch during the weekend: an action movie, a comedy, or a drama. However, she wants to watch the same drama movie three times, an action movie once and a comedy movie also once. In how many different ways can she arrange these five screenings?

A. 6
B. 20
C. 24
D. 60
E. 120


The number of different ways Carly can watch Drama, Drama, Drama, Action, Comedy (DDDAC) is basically the number of arrangements of 5 letters DDDAC out of which 3 D's are identical, so it's \(\frac{5!}{3!}=20\).


Answer: B


Hi Bunuel,

The above explanation is perfect. Thank you.
However, if the question asks with respect to DDDAC, how many ways that 3Ds are NOT Together then how exactly should one approach?

I think: Total ways possible - when the 3Ds are together.
ie. 5!/3! - ?


In this case we should subtract from total ways, which is 20, the number of ways when 3 D's are together.

Consider 3 D's as one unit {DDD}. We'll have 3 units: {DDD}{A}{C}. The number of ways to arrange them is 3! = 6.

So, the answer in this case would be 20 - 6 = 14.

Hope it's clear.
_________________

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

Intern
Intern
avatar
Joined: 24 Aug 2015
Posts: 1
Re: M05-27 [#permalink]

Show Tags

New post 21 Sep 2015, 07:58
What is the rule for this type of combination problem? It doesn't seem to follow the fundamental counting rule (n!)/[(r!)(n-r)!].... or does it?
Intern
Intern
avatar
Joined: 01 Aug 2015
Posts: 1
GMAT ToolKit User
Re: M05-27 [#permalink]

Show Tags

New post 25 Sep 2015, 12:35
The answer is D
Intern
Intern
User avatar
Joined: 14 Mar 2015
Posts: 35
Schools: ISB '18
M05-27 [#permalink]

Show Tags

New post 28 Sep 2015, 10:38
patrickmhoy wrote:
What is the rule for this type of combination problem? It doesn't seem to follow the fundamental counting rule (n!)/[(r!)(n-r)!].... or does it?


The first thing in Combinatorics is to figure out whether the problem is of Permutation or Combination.

This problem asks for the "arrangement", so this is clearly a Permutation problem. But the author also says that one type of movie (Drama) has to be watched thrice.

So possible arrangements are -

DDDAC
ADDDC
ACDDD
DDACD
...
..
and so on.

Now you should see here that the 3 Ds are same, so their arrangement, when they are placed together, doesn't really matter.

So, like Bunuel has mentioned in the official solution, the total number of arrangements for n objects with repetition, in which object-1 repeats n1 times, object-2 repeats n2 times, object-3 repeats n3 times and so on, can be given from the formula -
n!/(n1! *n2! * n3! .....)
= 5!/(3! * 1! * 1*)
= 5!/3!
= 20
_________________

It ain’t about how hard you hit. It’s about how hard you can get hit and keep moving forward;
how much you can take and keep moving forward.

That’s how winning is done!

Intern
Intern
avatar
Joined: 07 Oct 2015
Posts: 1
Re: M05-27 [#permalink]

Show Tags

New post 11 Nov 2015, 08:08
I find this question vague because nowhere in the question does it state that she wants to watch the three drama movies after each other, and since we are taught not to assume anything in the GMAT handling of questions shouldnt we assume that she can watch DACDD , DDACD, ADCDD etc...

doesnt seem logical to treat {DDD} as a 'glued' set since it doesnt state she wants to watch them three times IN SEQUENCE...

Anyone agree with my reasoning?

thanks
Intern
Intern
avatar
B
Joined: 24 Nov 2014
Posts: 3
Schools: Alberta'18
GMAT ToolKit User
Re: M05-27 [#permalink]

Show Tags

New post 20 Jul 2016, 06:27
The answer is for 3 Drama screenings and not 3 consecutive Drama screening.

If question had mentioned 3 consecutive drama screening then answer would have been 6. (consider 3 Ds as a single entity and A and C so total 3 entities which can be arranged in 3! ways).

Hope its clear !!!
Intern
Intern
avatar
B
Joined: 26 Sep 2016
Posts: 23
Reviews Badge
Re: M05-27 [#permalink]

Show Tags

New post 11 Apr 2017, 07:59
Hey

Not sure i understand why we divide by 3!, what are we getting rid of? What is the general idea behind "repetitions allowed"? Can someone explain this problem according to filling spaces method?
Intern
Intern
avatar
B
Joined: 01 Nov 2017
Posts: 11
CAT Tests
Re: M05-27 [#permalink]

Show Tags

New post 15 Jan 2018, 06:26
As we have 5 different movies (DDDAC), I applied the formula (n-1)!, which results in (5-1)!=4!=1*2*3*4=24.

Why is this wrong? Where am I going in the wrong direction?
Expert Post
Math Expert
User avatar
D
Joined: 02 Aug 2009
Posts: 5663
Re: M05-27 [#permalink]

Show Tags

New post 15 Jan 2018, 06:35
Gregsterh wrote:
As we have 5 different movies (DDDAC), I applied the formula (n-1)!, which results in (5-1)!=4!=1*2*3*4=24.

Why is this wrong? Where am I going in the wrong direction?


(n-1)! is used in a circular combination .... say n person sitting around a circular table. (n-1)!

but here there are 5 items out of which three are of on ekind..
formula is 5!/3!.. div by 3! is because these three can be arranged among themselves in 3! ways and so to avoid repetitions, we div by 3!
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html


BANGALORE/-

Re: M05-27   [#permalink] 15 Jan 2018, 06:35
Display posts from previous: Sort by

M05-27

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

Moderators: chetan2u, Bunuel



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®.