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

It is currently 19 Aug 2014, 23:26

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Tom is arranging his marble collection in a collectors case.

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
2 KUDOS received
Manager
Manager
avatar
Status: Keep fighting!
Affiliations: IIT Madras
Joined: 31 Jul 2010
Posts: 238
WE 1: 2+ years - Programming
WE 2: 3+ years - Product developement,
WE 3: 2+ years - Program management
Followers: 4

Kudos [?]: 155 [2] , given: 104

Tom is arranging his marble collection in a collectors case. [#permalink] New post 10 Oct 2010, 02:08
2
This post received
KUDOS
4
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  55% (medium)

Question Stats:

45% (03:19) correct 55% (02:28) wrong based on 56 sessions
Tom is arranging his marble collection in a collectors case. He has five identical cat-eyes, five identical sulphides, and three identical agates. If he can fit exactly five marbles into the case and must have at least one of each type, how many different ways can he arrange the case?

(A) 120
(B) 150
(C) 420
(D) 1,260
(E) 1,680

Don't forget KUDOS if you like this.
[Reveal] Spoiler: OA

Last edited by hemanthp on 10 Oct 2010, 02:36, edited 1 time in total.
3 KUDOS received
Retired Moderator
User avatar
Joined: 02 Sep 2010
Posts: 807
Location: London
Followers: 77

Kudos [?]: 464 [3] , given: 25

GMAT ToolKit User GMAT Tests User Reviews Badge
Re: Tom's collection [#permalink] New post 10 Oct 2010, 02:16
3
This post received
KUDOS
hemanthp wrote:
Tom is arranging his marble collection in a collectors case. He has five identical cat-eyes, five identical sulphides, and three identical agates. If he can fit exactly five marbles into the case and must have at least one of each type, how many different ways can he arrange the case?

(A) 120
(B) 150
(C) 420
(D) 1,260
(E) 1,680

I dont agree with the OA. Lets discuss.


Given the constraints, there is 2 ways to choose the stones :

1) Take 2 each of 2 types and 1 of the third type
3 ways to choose the type for which 1 stone is to be taken
Ways to arrange = 5!/(2!x2!) = 30
Total = 30 x 3 = 90

2) Take 3 of 1 type, one each of the other types
3 ways to choose the type for which 3 stones are to be taken
Ways to arrange = 5!/3! = 20
Total = 20 x 3 = 60

So net number of ways = 150

Answer is (b)
_________________

Math write-ups
1) Algebra-101 2) Sequences 3) Set combinatorics 4) 3-D geometry

My GMAT story

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Manager
Manager
avatar
Status: Keep fighting!
Affiliations: IIT Madras
Joined: 31 Jul 2010
Posts: 238
WE 1: 2+ years - Programming
WE 2: 3+ years - Product developement,
WE 3: 2+ years - Program management
Followers: 4

Kudos [?]: 155 [0], given: 104

Re: Tom's collection [#permalink] New post 10 Oct 2010, 02:32
Damn... silly mistakes again. Thank you Shrouded. Feel embarrassed for making a mistake and posting it out thinking I was right. I feel I should delete the post.
Expert Post
4 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 19020
Followers: 3358

Kudos [?]: 24331 [4] , given: 2676

Re: Tom's collection [#permalink] New post 10 Oct 2010, 04:15
4
This post received
KUDOS
Expert's post
hemanthp wrote:
Tom is arranging his marble collection in a collectors case. He has five identical cat-eyes, five identical sulphides, and three identical agates. If he can fit exactly five marbles into the case and must have at least one of each type, how many different ways can he arrange the case?

(A) 120
(B) 150
(C) 420
(D) 1,260
(E) 1,680

Don't forget KUDOS if you like this.


We have that 3 marbles CSA must be in the collection case as he must have at least one of each type.

Then five chosen marbles could be:

1. CSA-XX - meaning that other 2 marbles are the same (for example CSA-CC):
\frac{5!}{3!}*C^1_3=60 (C^1_3 choosing which marble out of the 3 will be X and \frac{5!}{3!} arranging 5 marbles our of which 3 are identical).

2. CSA-XY - meaning that other 2 marbles are not the same (for example CSA-CS):
\frac{5!}{2!2!}*C^2_3=60 (C^2_3 choosing which 2 marbles out of 3 will be X and Y and \frac{5!}{2!2!} arranging 5 marbles our of which 2 and other 2 are identical).

Total: 60+90=150.

Answer: B.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Manager
Manager
avatar
Joined: 17 Apr 2010
Posts: 109
Followers: 2

Kudos [?]: 50 [0], given: 12

GMAT ToolKit User GMAT Tests User
Re: Tom's collection [#permalink] New post 10 Oct 2010, 11:14
Thanks for the question and Explanation. Kudos to both of you
SVP
SVP
User avatar
Joined: 09 Sep 2013
Posts: 2064
Followers: 178

Kudos [?]: 34 [0], given: 0

Premium Member
Re: Tom is arranging his marble collection in a collectors case. [#permalink] New post 03 Dec 2013, 06:50
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

Intern
Intern
avatar
Joined: 02 Oct 2013
Posts: 12
Followers: 0

Kudos [?]: 4 [0], given: 6

Re: Tom is arranging his marble collection in a collectors case. [#permalink] New post 04 Dec 2013, 15:32
Doesn't the order of the stones matter in this problem? It says "how many different ways could he arrange the case?".
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 19020
Followers: 3358

Kudos [?]: 24331 [0], given: 2676

Re: Tom is arranging his marble collection in a collectors case. [#permalink] New post 05 Dec 2013, 01:53
Expert's post
PKUTNEY wrote:
Doesn't the order of the stones matter in this problem? It says "how many different ways could he arrange the case?".


Yes, it does and each solution above talks about arrangement of the marbles after selecting. For example, check here: tom-is-arranging-his-marble-collection-in-a-collectors-case-102588.html#p797440

Hope it helps.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Manager
Manager
User avatar
Status: Work hard in silence, let success make the noise
Joined: 25 Nov 2013
Posts: 160
Location: India
Concentration: Finance, General Management
GMAT 1: 540 Q50 V15
GMAT 2: 640 Q50 V27
GPA: 3.11
WE: Consulting (Computer Software)
Followers: 5

Kudos [?]: 29 [0], given: 84

Re: Tom is arranging his marble collection in a collectors case. [#permalink] New post 10 Dec 2013, 09:31
Either we could have 2,2,1 combo or 3,1,1 combo. Each of these combos in turn have 3 different cases.
So, required answer is 3*(5!/3!) + 3*(5!/2!*2!) = 150.

So, the correct answer is B.
_________________

Sahil Chaudhary
If you find this post helpful, please take a moment to click on the "+1 KUDOS" icon.
My IELTS 7.5 Experience
From 540 to 640...Done with GMAT!!!
http://www.sahilchaudhary007.blogspot.com

Re: Tom is arranging his marble collection in a collectors case.   [#permalink] 10 Dec 2013, 09:31
    Similar topics Author Replies Last post
Similar
Topics:
Experts publish their posts in the topic Collection of Questions arranged in GMAT like pattern: any1? ROckHIsT 1 02 Jan 2014, 03:58
Tom loves his mareting management job radioguy 1 22 Dec 2013, 06:37
1 Experts publish their posts in the topic In his pocket, a boy has 3 red marbles, 4 blue marbles, and timmaxwell8 6 12 Oct 2009, 11:40
Marbles sandalphon 17 18 Dec 2005, 07:40
Rembrandt so treasured his collection of Islamic portraits sgrover 5 14 Sep 2005, 06:46
Display posts from previous: Sort by

Tom is arranging his marble collection in a collectors case.

  Question banks Downloads My Bookmarks Reviews Important topics  


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

Powered by phpBB © phpBB Group and phpBB SEO

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®.