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

It is currently 23 Aug 2014, 09:22

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

An insect has one shoe and one sock for each of its twelve

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
2 KUDOS received
Manager
Manager
User avatar
Joined: 22 Jul 2008
Posts: 95
Location: Bangalore,Karnataka
Followers: 3

Kudos [?]: 49 [2] , given: 11

An insect has one shoe and one sock for each of its twelve [#permalink] New post 02 Dec 2009, 00:35
2
This post received
KUDOS
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

37% (01:56) correct 63% (01:25) wrong based on 51 sessions
An insect has one shoe and one sock for each of its twelve legs. In how many different orders can the insect put on its socks and shoes, assuming that, on each leg, the sock must be put on before the shoe?

A. 2^{12} * 12!

B. \frac{24!}{12!^2}

C. \frac{24!}{2^{12}}

D. 24!

E. 24!* 12^2
[Reveal] Spoiler: OA
Intern
Intern
avatar
Joined: 25 Nov 2009
Posts: 30
Followers: 0

Kudos [?]: 9 [0], given: 4

Re: Insect [#permalink] New post 02 Dec 2009, 00:40
Does the order matter considering 1 leg can only have 1 sock and 1 shoe and that the sock and shoe are not interchangeable?

I'm asking a genuine question, not trying to point anything out...
Expert Post
6 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 19052
Followers: 3375

Kudos [?]: 24590 [6] , given: 2680

Re: Insect [#permalink] New post 02 Dec 2009, 16:26
6
This post received
KUDOS
Expert's post
This is a very good question. +1.

Also I believe nothing like this will ever occur at real test, as this question is beyond the scope of GMAT.

Anyway here is my solution:

NOTE that each sock and shoe is "assigned" to a specific leg.

Imagine situation with no restriction, meaning no need to put the socks before the shoes. In this case the # of ways insect can put 24 items would be 24!. As we can choose to put ANY of 24 items first, then 23 items left, then 22 and so on.

Next step. On EACH leg we can put either sock OR shoe first. But for EACH leg from 12, only one order is correct WITH restriction: sock first then shoe. For one leg chances of correct order is 1/2, for two legs 1/2^2, similarly for 12 legs chances of correct order would 1/2^12.

So we get that for the total # of ways, WITH NO RESTRICTION, which is 24!, only 1/2^12 is good WITH RESTRICTION.

So the final answer is 24!/2^12.

Answer: C.
_________________

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: 04 Nov 2009
Posts: 64
Schools: London Business School (int)
WE 1: Research
WE 2: Corporate Strat
Followers: 1

Kudos [?]: 13 [0], given: 1

Re: Insect [#permalink] New post 02 Dec 2009, 20:05
Trying to fully understand Bunuel's method.
When we arrange them all in 24! ways, leg could possibly have 1 shoe + 1 sock, 1 sock + 1 shoe, 2 socks or 2 shoes.

Do we not need to remove out the cases where the leg has only shoes or only socks before imposing the restriction and dividing by 2?
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 19052
Followers: 3375

Kudos [?]: 24590 [0], given: 2680

Re: Insect [#permalink] New post 03 Dec 2009, 04:11
Expert's post
4test1 wrote:
Trying to fully understand Bunuel's method.
When we arrange them all in 24! ways, leg could possibly have 1 shoe + 1 sock, 1 sock + 1 shoe, 2 socks or 2 shoes.

Do we not need to remove out the cases where the leg has only shoes or only socks before imposing the restriction and dividing by 2?


Leg can not have two socks or two shoes, as each leg has its specific shoe or specific sock. Meaning that shoe and sock is fixed to a certain leg, hence insect can put on one leg ONLY the sock and shoe of THIS leg.

Hope it's clear.
_________________

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
Joined: 22 Jul 2008
Posts: 95
Location: Bangalore,Karnataka
Followers: 3

Kudos [?]: 49 [0], given: 11

Re: Insect [#permalink] New post 03 Dec 2009, 05:51
Thanks Bunuel.. I guessed so that it will be out of GMAT scope.
Manager
Manager
User avatar
Joined: 29 Jun 2011
Posts: 76
Followers: 3

Kudos [?]: 11 [0], given: 47

Re: Insect [#permalink] New post 02 Jul 2011, 07:25
my goodness...this is some heavy question...and i thought i was good at combinations!
bunuel's method of combining combinatorics and probability is sheer genius.
+1!
_________________

It matters not how strait the gate,
How charged with punishments the scroll,
I am the master of my fate :
I am the captain of my soul.
~ William Ernest Henley

Manager
Manager
avatar
Joined: 03 Aug 2011
Posts: 241
Location: United States
Concentration: General Management, Entrepreneurship
GMAT 1: 750 Q49 V44
GPA: 3.38
WE: Engineering (Computer Software)
Followers: 1

Kudos [?]: 39 [0], given: 12

Re: Insect [#permalink] New post 16 Aug 2011, 14:12
*found an error in what i did, will repost
Manager
Manager
avatar
Status: Do till 740 :)
Joined: 13 Jun 2011
Posts: 104
Concentration: Strategy, General Management
GMAT 1: 460 Q35 V20
GPA: 3.6
WE: Consulting (Computer Software)
Followers: 0

Kudos [?]: 5 [0], given: 18

GMAT ToolKit User
Re: Insect [#permalink] New post 14 Sep 2011, 13:03
Quote:
Next step. On EACH leg we can put either sock OR shoe first. But for EACH leg from 12, only one order is correct WITH restriction: sock first then shoe. For one leg chances of correct order is 1/2, for two legs 1/2^2, similarly for 12 legs chances of correct order would 1/2^12.



Hi bunel,
can you please explain the 1/2 part may be with a simpler example.I'm dumb :)
1 KUDOS received
Manager
Manager
avatar
Joined: 16 Feb 2011
Posts: 196
Schools: ABCD
Followers: 1

Kudos [?]: 29 [1] , given: 78

GMAT Tests User
Re: Insect [#permalink] New post 01 Aug 2012, 12:36
1
This post received
KUDOS
Bunuel wrote:
This is a very good question. +1.

Also I believe nothing like this will ever occur at real test, as this question is beyond the scope of GMAT.

Anyway here is my solution:

NOTE that each sock and shoe is "assigned" to a specific leg.

Imagine situation with no restriction, meaning no need to put the socks before the shoes. In this case the # of ways insect can put 24 items would be 24!. As we can choose to put ANY of 24 items first, then 23 items left, then 22 and so on.

Next step. On EACH leg we can put either sock OR shoe first. But for EACH leg from 12, only one order is correct WITH restriction: sock first then shoe. For one leg chances of correct order is 1/2, for two legs 1/2^2, similarly for 12 legs chances of correct order would 1/2^12.

So we get that for the total # of ways, WITH NO RESTRICTION, which is 24!, only 1/2^12 is good WITH RESTRICTION.

So the final answer is 24!/2^12.

Answer: C.



Bunuel,
Sorry to open this thread. Why wouldn't it be 12! * 12!? For each of the legs, there are 12 possible socks = 12!. Once the socks are chosen, there are 12 possible shoes = 12!

Therefore, using Fund. Principle of counting, the total permutations should be (12!)^2 ? Correct?
Intern
Intern
avatar
Joined: 15 Apr 2012
Posts: 8
Followers: 0

Kudos [?]: 0 [0], given: 8

Re: Insect [#permalink] New post 04 Aug 2012, 22:16
voodoochild wrote:
Bunuel wrote:
This is a very good question. +1.

Also I believe nothing like this will ever occur at real test, as this question is beyond the scope of GMAT.

Anyway here is my solution:

NOTE that each sock and shoe is "assigned" to a specific leg.

Imagine situation with no restriction, meaning no need to put the socks before the shoes. In this case the # of ways insect can put 24 items would be 24!. As we can choose to put ANY of 24 items first, then 23 items left, then 22 and so on.

Next step. On EACH leg we can put either sock OR shoe first. But for EACH leg from 12, only one order is correct WITH restriction: sock first then shoe. For one leg chances of correct order is 1/2, for two legs 1/2^2, similarly for 12 legs chances of correct order would 1/2^12.

So we get that for the total # of ways, WITH NO RESTRICTION, which is 24!, only 1/2^12 is good WITH RESTRICTION.

So the final answer is 24!/2^12.

Answer: C.



Bunuel,
Sorry to open this thread. Why wouldn't it be 12! * 12!? For each of the legs, there are 12 possible socks = 12!. Once the socks are chosen, there are 12 possible shoes = 12!

Therefore, using Fund. Principle of counting, the total permutations should be (12!)^2 ? Correct?



hi voodoochild,
For each of the legs, there are possible 24 objects (12 shoes+12 socks) that can be worn. therefore 24!
With the restriction given, in half of the orders, a shoe would be worn before sock and in the other half, a sock would be worn before the shoe .
C seems to be the only option with that restriction.
IMO
24!/2 would be the answer. I dont understand the need to restrict the order i.e (1/2)^12 times.
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 19052
Followers: 3375

Kudos [?]: 24590 [0], given: 2680

Re: An insect has one shoe and one sock for each of its twelve [#permalink] New post 05 Aug 2012, 00:45
Expert's post
Director
Director
User avatar
Joined: 22 Mar 2011
Posts: 613
WE: Science (Education)
Followers: 68

Kudos [?]: 500 [0], given: 43

GMAT Tests User
Re: An insect has one shoe and one sock for each of its twelve [#permalink] New post 05 Aug 2012, 01:18
Bunuel wrote:
OA for this question is C.

BUT: this is question is out of the scope of GMAT, so I wouldn't worry about it at all. No need to waste much of your time on it.


Hi Bunuel,

I think this is an advanced version of a question I saw on the forum before... something about people standing in a queue and it was about X should stand in front of Y (there were specific names). There were n (some specific number) people altogether, so the number of possibilities was n!/2 (in half of them X was in front of Y and in the other half X wasn't). Can you pull out the question?
The insect question would be a version of the queue question, for example with 24 couples (husbands and wives), and asking for the number of possibilities in which each wife stands in front of her husband.
Or in general: total of n people in a queue, k couples (2k \leq n), each wife standing in front of her husband - number of possible arrangements is n!/(2^k).

It could be a +700 question on a test...don't you think?
_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 19052
Followers: 3375

Kudos [?]: 24590 [0], given: 2680

Re: An insect has one shoe and one sock for each of its twelve [#permalink] New post 05 Aug 2012, 01:28
Expert's post
EvaJager wrote:
Bunuel wrote:
OA for this question is C.

BUT: this is question is out of the scope of GMAT, so I wouldn't worry about it at all. No need to waste much of your time on it.


Hi Bunuel,

I think this is an advanced version of a question I saw on the forum before... something about people standing in a queue and it was about X should stand in front of Y (there were specific names). There were n (some specific number) people altogether, so the number of possibilities was n!/2 (in half of them X was in front of Y and in the other half X wasn't). Can you pull out the question?
The insect question would be a version of the queue question, for example with 24 couples (husbands and wives), and asking for the number of possibilities in which each wife stands in front of her husband.
Or in general: total of n people in a queue, k couples (2k \leq n), each wife standing in front of her husband - number of possible arrangements is n!/(2^k).

It could be a +700 question on a test...don't you think?


GMAT combination/probability questions are fairly straightforward, so frankly speaking I think that there is 0 chances for this kind of question appearing on the real test.

As for the the question you are talking about, there are several of that kind:
six-mobsters-have-arrived-at-the-theater-for-the-premiere-of-the-126151.html
susan-john-daisy-tim-matt-and-kim-need-to-be-seated-in-130743.html
meg-and-bob-are-among-the-5-participants-in-a-cycling-race-58095.html
in-how-many-different-ways-can-the-letters-a-a-b-91460.html
mary-and-joe-are-to-throw-three-dice-each-the-score-is-the-126407.html
goldenrod-and-no-hope-are-in-a-horse-race-with-6-contestants-82214.html
in-how-many-ways-can-a-teacher-in-a-kindergarten-school-136369.html
_________________

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

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 19052
Followers: 3375

Kudos [?]: 24590 [0], given: 2680

Re: An insect has one shoe and one sock for each of its twelve [#permalink] New post 15 Apr 2013, 00:23
Expert's post
obs23 wrote:
Bunuel wrote:
OA for this question is C.

BUT: this question is out of the scope of GMAT, so I wouldn't worry about it at all. No need to waste much of your time on it.


Bunuel, this is tough indeed. Just for the peace of mind, I thought of this question as Leg 1 has 12 socks and 12 shoes, Leg 2 has 11 socks and 11 shoes...etc. Again, it feels a bit more intuitive...what do you think of this approach? I am struggling to put it into the answers and come up with an algebraic way to get to the answer...Would not it be (12*12)+(11*11)+(10*10)...(1*1)? Please share your thoughts...


Hi,

Solution is given here: an-insect-has-one-shoe-and-one-sock-for-each-of-its-twelve-87503.html#p658176

The question is out of the scope of GMAT, so I wouldn't worry about it AT ALL and wouldn't recommend to spend any time studying it.

Topic locked.

Regards,
Bunuel.
_________________

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

Re: An insect has one shoe and one sock for each of its twelve   [#permalink] 15 Apr 2013, 00:23
    Similar topics Author Replies Last post
Similar
Topics:
7 Experts publish their posts in the topic Each of the following equations has at least one solution marcusaurelius 26 12 May 2010, 09:12
6 Experts publish their posts in the topic Each of the following equations has at least one solution vigneshpandi 9 01 Oct 2009, 16:45
1 Experts publish their posts in the topic There are n different size pairs of shoes in the box. One lexis 18 02 May 2008, 09:04
The auto industry has experienced one of its most arjsingh1976 2 25 Nov 2006, 02:16
The auto industry has experienced one of its most Antmavel 3 18 Oct 2004, 07:55
Display posts from previous: Sort by

An insect has one shoe and one sock for each of its twelve

  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®.