It is currently 17 Jan 2018, 18:21

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

Jill is dividing her ten-person class into two teams of eq

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

Hide Tags

2 KUDOS received
Manager
Manager
avatar
Joined: 09 Feb 2013
Posts: 120

Kudos [?]: 1246 [2], given: 17

Jill is dividing her ten-person class into two teams of eq [#permalink]

Show Tags

New post 28 Feb 2013, 04:25
2
This post received
KUDOS
7
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

43% (01:23) correct 57% (01:30) wrong based on 203 sessions

HideShow timer Statistics

Jill is dividing her ten-person class into two teams of equal size for a basketball game. If no one will sit out, how many different match-ups between the two teams are possible?

A. 10
B. 25
C. 126
D. 252
E. 630
[Reveal] Spoiler: OA

_________________

Kudos will encourage many others, like me.
Good Questions also deserve few KUDOS.


Last edited by Bunuel on 28 Feb 2013, 05:14, edited 1 time in total.
Edited the question.

Kudos [?]: 1246 [2], given: 17

Expert Post
2 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 43312

Kudos [?]: 139328 [2], given: 12783

Re: Jill is dividing her ten-person class into two teams of eq [#permalink]

Show Tags

New post 28 Feb 2013, 05:29
2
This post received
KUDOS
Expert's post
2
This post was
BOOKMARKED
emmak wrote:
Jill is dividing her ten-person class into two teams of equal size for a basketball game. If no one will sit out, how many different match-ups between the two teams are possible?

A. 10
B. 25
C. 126
D. 252
E. 630


There should be 5 people in each group. We can divide a group of 10 people into 2 teams of 5 in \(\frac{C^5_{10}*C^5_5}{2!}=126\) ways (dividing by 2! because the order of the groups doesn't matter).

Answer: C.

For more on this check:
a-group-of-8-friends-want-to-play-doubles-tennis-how-many-55369.html
in-how-many-different-ways-can-a-group-of-9-people-be-85993.html
probability-88685.html
probability-85993.html
combination-55369.html
sub-committee-86346.html

Hope it helps.
_________________

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

Kudos [?]: 139328 [2], given: 12783

Senior Manager
Senior Manager
User avatar
Joined: 23 Oct 2010
Posts: 379

Kudos [?]: 418 [0], given: 73

Location: Azerbaijan
Concentration: Finance
Schools: HEC '15 (A)
GMAT 1: 690 Q47 V38
GMAT ToolKit User
Re: Jill is dividing her ten-person class into two teams of eq [#permalink]

Show Tags

New post 02 Mar 2013, 10:47
here is a formula -http://gmatclub.com/forum/a-group-of-8-friends-want-to-play-doubles-tennis-how-many-55369.html#p689312
The number of ways in which mn different items can be divided equally into m groups, each containing n objects and the order of the groups is not important is -
(mn)!/(n!)^m*m!


10! /((5!)^2*2!) =126
_________________

Happy are those who dream dreams and are ready to pay the price to make them come true

I am still on all gmat forums. msg me if you want to ask me smth

Kudos [?]: 418 [0], given: 73

Expert Post
2 KUDOS received
EMPOWERgmat Instructor
User avatar
P
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 10696

Kudos [?]: 3773 [2], given: 173

Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Re: Jill is dividing her ten-person class into two teams of eq [#permalink]

Show Tags

New post 23 Apr 2015, 14:42
2
This post received
KUDOS
Expert's post
Hi All,

This question tests your knowledge of the Combination Formula, but it comes with a rare "twist" that most people don't realize. Here's a bit more information on that "twist":

With 10 players, the process of figuring out how many groups of 5 can be formed is pretty straight-forward....

10C5 = 10!/(5!5!) = 256 possible groups of 5

Once forming that first group of 5, the remaining 5 players would all be placed on the second team by default.

The 'twist' is that the two teams of 5 can "show up" in either order:

For example, if we call the two teams of 5 players: A,B,C,D,E and F,G,H,I,J

ABCDE vs. FGHIJ

is the SAME match-up as....

FGHIJ vs. ABCDE

So we are NOT allowed to count that matchup twice. This means we have to divide the 256 by 2.

Final Answer:
[Reveal] Spoiler:
C


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 [?]: 3773 [2], given: 173

Manager
Manager
avatar
B
Joined: 30 Aug 2017
Posts: 94

Kudos [?]: 2 [0], given: 183

Location: Korea, Republic of
GMAT 1: 700 Q51 V31
GPA: 3.68
Re: Jill is dividing her ten-person class into two teams of eq [#permalink]

Show Tags

New post 04 Oct 2017, 19:14
good question.

When we pick 5 people out of 10 people(10C5), we can make each side of team simultaneously.
And We have to devide by 2 to avoid duplication.

Kudos [?]: 2 [0], given: 183

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 43312

Kudos [?]: 139328 [0], given: 12783

Re: Jill is dividing her ten-person class into two teams of eq [#permalink]

Show Tags

New post 30 Dec 2017, 11:56
emmak wrote:
Jill is dividing her ten-person class into two teams of equal size for a basketball game. If no one will sit out, how many different match-ups between the two teams are possible?

A. 10
B. 25
C. 126
D. 252
E. 630


VERITAS PREP OFFICIAL SOLUTION:

Correct Answer: (C)

This is a trickier spin on a basic combinatorics problem. Begin by asking how many groups of 5 can be created from a pool of 10 candidates. Order does not matter, so this is a combinations problem. Use the combinations formula: n!/(k!)(n-k)! That answer would be 10!/[(5!)(5!)] = 252. But (D) is a trap answer. The problem does not ask how many team arrangements are possible; it asks how many match-ups are possible. Each match-up consists of a team of five opposing the remaining five people. Therefore, each match-up involves two of the 252 teams. To find the number of match-ups, divide 252 in half for a total of 126. The correct answer is (C).
_________________

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

Kudos [?]: 139328 [0], given: 12783

Senior Manager
Senior Manager
User avatar
B
Joined: 27 Mar 2016
Posts: 346

Kudos [?]: 120 [0], given: 27

Location: United States (CO)
GMAT 1: 770 Q51 V44
GPA: 3.69
WE: Analyst (Consulting)
Re: Jill is dividing her ten-person class into two teams of eq [#permalink]

Show Tags

New post 30 Dec 2017, 15:09
I love questions like these which test your problem-solving skill rather than pure math. If you don't sit back to make sure your approach is on point before diving into the numbers, you'll likely pick the wrong answer. :)

Kudos [?]: 120 [0], given: 27

Expert Post
e-GMAT Representative
User avatar
S
Joined: 04 Jan 2015
Posts: 786

Kudos [?]: 2321 [0], given: 126

Re: Jill is dividing her ten-person class into two teams of eq [#permalink]

Show Tags

New post 31 Dec 2017, 07:49
emmak wrote:
Jill is dividing her ten-person class into two teams of equal size for a basketball game. If no one will sit out, how many different match-ups between the two teams are possible?

A. 10
B. 25
C. 126
D. 252
E. 630



A really good question and there is a high chance that a lot of people will mark 252 as the answer.

While grouping people or any item, we always need to take care of double counting. Also, whenever one sees options which are multiple of each other ( in this case 126 and 252),we should always double check our answers to make sure we have not made a mistake of double counting.

The best way to find out if one is making a mistake or not is to take small numbers and check it quickly. Let's say instead of 10, there were 2 people (A and B). In how many ways can you make two teams of equal size?

The answer is simple, right? It's 1. A in one team and B in the other. But if we use the formula, we will get 2C1 = 2, which is not correct, because of double counting, (A and B) and (B and A) have been considered different, which is not correct. Hence, to get the correct answer, we need to divide 2C1 by 2, which would give us 1.

In this question also, we need to do the same thing 10C5 would include a lot of repetitive cases, and we can get rid of them by dividing it by 2. Thus, the correct answer would be 10C5/2, which is Option C. :)


Regards,
Saquib
e-GMAT
Quant Expert
_________________












| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Kudos [?]: 2321 [0], given: 126

Senior Manager
Senior Manager
User avatar
G
Joined: 13 Apr 2013
Posts: 259

Kudos [?]: 94 [0], given: 682

Location: India
Concentration: International Business, Operations
Schools: ISB '19
GMAT 1: 480 Q38 V22
GPA: 3.01
WE: Engineering (Consulting)
Premium Member CAT Tests
Re: Jill is dividing her ten-person class into two teams of eq [#permalink]

Show Tags

New post 31 Dec 2017, 09:05
EgmatQuantExpert wrote:
emmak wrote:
Jill is dividing her ten-person class into two teams of equal size for a basketball game. If no one will sit out, how many different match-ups between the two teams are possible?

A. 10
B. 25
C. 126
D. 252
E. 630



A really good question and there is a high chance that a lot of people will mark 252 as the answer.

While grouping people or any item, we always need to take care of double counting. Also, whenever one sees options which are multiple of each other ( in this case 126 and 252),we should always double check our answers to make sure we have not made a mistake of double counting.

The best way to find out if one is making a mistake or not is to take small numbers and check it quickly. Let's say instead of 10, there were 2 people (A and B). In how many ways can you make two teams of equal size?
The answer is simple, right? It's 1. A in one team and B in the other. But if we use the formula, we will get 2C1 = 2, which is not correct, because of double counting, (A and B) and (B and A) have been considered different, which is not correct. Hence, to get the correct answer, we need to divide 2C1 by 2, which would give us 1.

In this question also, we need to do the same thing 10C5 would include a lot of repetitive cases, and we can get rid of them by dividing it by 2. Thus, the correct answer would be 10C5/2, which is Option C. :)


Regards,
Saquib
e-GMAT
Quant Expert


Good example used to check double counting. It cleared my mind quite nicely and I will check many trap answers this way. Thanks
_________________

"Success is not as glamorous as people tell you. It's a lot of hours spent in the darkness."

Kudos [?]: 94 [0], given: 682

Intern
Intern
avatar
B
Joined: 16 Jul 2016
Posts: 33

Kudos [?]: 10 [0], given: 2

Jill is dividing her ten-person class into two teams of eq [#permalink]

Show Tags

New post 31 Dec 2017, 12:35
One good idea is to start with a smaller case. Suppose there are 4 teams. A,B,C, and D

The possibilities of combinations taken two at a time are

AB
AC
AD

BC
BD

CD

I have color coated the "pairs." If AB is selected they must face off against CD. If CD is selected they must face off against AB. So those two combinations cannot be counted twice. This leads us to reason we should take a combination of 10 things taken 5 at a time and then divide by 2 to account for matching "pairs."


{(10)(9)(8)(7)(6)}/{(5)(4)(3)(2)(1)(2)}=126

Kudos [?]: 10 [0], given: 2

Jill is dividing her ten-person class into two teams of eq   [#permalink] 31 Dec 2017, 12:35
Display posts from previous: Sort by

Jill is dividing her ten-person class into two teams of eq

  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®.