It is currently 18 Jan 2018, 21:57

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

There are 10 children in a company's day-care center, and a pair of

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

Hide Tags

Manager
Manager
User avatar
Joined: 17 Aug 2006
Posts: 86

Kudos [?]: 22 [0], given: 0

There are 10 children in a company's day-care center, and a pair of [#permalink]

Show Tags

New post 12 Nov 2008, 05:36
7
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

88% (00:23) correct 13% (00:20) wrong based on 272 sessions

HideShow timer Statistics

There are 10 children in a company's day-care center, and a pair of children is to be selected to play a game. At most, how many different pairs are possible?

A) 100
B) 90
C) 50
D) 45
E) 25
[Reveal] Spoiler: OA

Last edited by Bunuel on 04 Mar 2015, 01:59, edited 2 times in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.

Kudos [?]: 22 [0], given: 0

Expert Post
1 KUDOS received
CEO
CEO
User avatar
B
Joined: 17 Nov 2007
Posts: 3583

Kudos [?]: 4795 [1], given: 360

Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
GMAT ToolKit User Premium Member
Re: There are 10 children in a company's day-care center, and a pair of [#permalink]

Show Tags

New post 12 Nov 2008, 05:44
1
This post received
KUDOS
Expert's post
2
This post was
BOOKMARKED
First way

1. first child out of 10 - 10 possibilities
2. second child out of 9 - 9 possibilities. the total number of pairs = 9*10=90
3. exclude xy yx cases: 90/2=45

Second way

N=10C2=10!/(8!2!)=10*9/2=45
_________________

HOT! GMAT TOOLKIT 2 (iOS) / GMAT TOOLKIT (Android) - The OFFICIAL GMAT CLUB PREP APP, a must-have app especially if you aim at 700+ | PrepGame

Kudos [?]: 4795 [1], given: 360

Expert Post
1 KUDOS received
EMPOWERgmat Instructor
User avatar
P
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 10707

Kudos [?]: 3777 [1], given: 173

Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Re: There are 10 children in a company's day-care center, and a pair of [#permalink]

Show Tags

New post 03 Mar 2015, 21:49
1
This post received
KUDOS
Expert's post
2
This post was
BOOKMARKED
Hi All,

This is an example of a fairly-straightforward Combinations question. It asks how many different pairs of children (meaning "sets of 2") are there that can be selected from a group of 10 children. In these situations, the ORDER of the two children does not matter, so if 'child A' plays 'child B' then that pair is the SAME as when 'child B' plays 'child A.' As such, you are NOT supposed to count that pairing twice. The Combinations Formula removes all of those duplicate pairs.

Combinations = N!/[K!(N-K)!] Where N is the total number of children and K is the number that you are going to pick.

Here, we have N = 10 and K = 2

10!/[2!8!] = (10)(9)/(2)(1) = 45 different pairs of 2 children.

Final Answer:
[Reveal] Spoiler:
D


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!***********************

Kudos [?]: 3777 [1], given: 173

Senior Manager
Senior Manager
User avatar
Status: Math is psycho-logical
Joined: 07 Apr 2014
Posts: 432

Kudos [?]: 145 [0], given: 169

Location: Netherlands
GMAT Date: 02-11-2015
WE: Psychology and Counseling (Other)
Re: There are 10 children in a company's day-care center, and a pair of [#permalink]

Show Tags

New post 04 Mar 2015, 05:00
Hello all,

I also did it like this:

10 children, one pair (2 children) selected and 8 children not:

10!/2!*8! = 9 * 10 / 1*2 = 90 / 2 = 45.

However, if we want to use pairs instead of the number of children, could we also say that out of the 5 pairs we are selecting 1 pair? And how would this go using combinations?

Kudos [?]: 145 [0], given: 169

Expert Post
Math Expert
User avatar
D
Joined: 02 Aug 2009
Posts: 5528

Kudos [?]: 6427 [0], given: 122

Re: There are 10 children in a company's day-care center, and a pair of [#permalink]

Show Tags

New post 04 Mar 2015, 05:05
pacifist85 wrote:
Hello all,

I also did it like this:

10 children, one pair (2 children) selected and 8 children not:

10!/2!*8! = 9 * 10 / 1*2 = 90 / 2 = 45.

However, if we want to use pairs instead of the number of children, could we also say that out of the 5 pairs we are selecting 1 pair? And how would this go using combinations?



hi pacifist,
the meaning of question will change if you write out of the 5 pairs we are selecting 1 pair?..
it means each pair is a separate identity and you have to choose one out of it ..
the ans will be 5c1=5...
_________________

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/-

Kudos [?]: 6427 [0], given: 122

Senior Manager
Senior Manager
User avatar
Status: Math is psycho-logical
Joined: 07 Apr 2014
Posts: 432

Kudos [?]: 145 [0], given: 169

Location: Netherlands
GMAT Date: 02-11-2015
WE: Psychology and Counseling (Other)
There are 10 children in a company's day-care center, and a pair of [#permalink]

Show Tags

New post 04 Mar 2015, 05:09
chetan2u wrote:
pacifist85 wrote:
Hello all,

I also did it like this:

10 children, one pair (2 children) selected and 8 children not:

10!/2!*8! = 9 * 10 / 1*2 = 90 / 2 = 45.

However, if we want to use pairs instead of the number of children, could we also say that out of the 5 pairs we are selecting 1 pair? And how would this go using combinations?



hi pacifist,
the meaning of question will change if you write out of the 5 pairs we are selecting 1 pair?..
it means each pair is a separate identity and you have to choose one out of it ..
the ans will be 5c1=5...


Yes, I also tested it and ended up with 5. But I wnted to see if there would be another approach to correct for it. For example, 5*9=45. But is this logical?

Kudos [?]: 145 [0], given: 169

Expert Post
1 KUDOS received
Math Expert
User avatar
D
Joined: 02 Aug 2009
Posts: 5528

Kudos [?]: 6427 [1], given: 122

Re: There are 10 children in a company's day-care center, and a pair of [#permalink]

Show Tags

New post 04 Mar 2015, 05:19
1
This post received
KUDOS
Expert's post
pacifist85 wrote:
chetan2u wrote:
pacifist85 wrote:
Hello all,

I also did it like this:

10 children, one pair (2 children) selected and 8 children not:

10!/2!*8! = 9 * 10 / 1*2 = 90 / 2 = 45.

However, if we want to use pairs instead of the number of children, could we also say that out of the 5 pairs we are selecting 1 pair? And how would this go using combinations?



hi pacifist,
the meaning of question will change if you write out of the 5 pairs we are selecting 1 pair?..
it means each pair is a separate identity and you have to choose one out of it ..
the ans will be 5c1=5...


Yes, I also tested it and ended up with 5. But I wnted to see if there would be another approach to correct for it. For example, 5*9=45. But is this logical?

no pacifist, it will not be correct.
_________________

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/-

Kudos [?]: 6427 [1], given: 122

Intern
Intern
avatar
Joined: 01 Apr 2015
Posts: 6

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

Re: There are 10 children in a company's day-care center, and a pair of [#permalink]

Show Tags

New post 01 Apr 2015, 02:38
Solving tricky questions like this is really difficult until you do not have taken good basic educations and that is why I have decided to send my daughter to Phoenix kindergarten for her better future.

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

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 14241

Kudos [?]: 291 [0], given: 0

Premium Member
Re: There are 10 children in a company's day-care center, and a pair of [#permalink]

Show Tags

New post 13 Dec 2017, 17:30
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

Kudos [?]: 291 [0], given: 0

Re: There are 10 children in a company's day-care center, and a pair of   [#permalink] 13 Dec 2017, 17:30
Display posts from previous: Sort by

There are 10 children in a company's day-care center, and a pair of

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


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®.