Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 18 Jul 2019, 10:30

### 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

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

# A group of 12 people who have never met are in a classroom. How many

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 56256
A group of 12 people who have never met are in a classroom. How many  [#permalink]

### Show Tags

03 Jan 2019, 09:34
00:00

Difficulty:

25% (medium)

Question Stats:

73% (00:59) correct 28% (01:33) wrong based on 54 sessions

### HideShow timer Statistics

A group of 12 people who have never met are in a classroom. How many handshakes are exchanged if each pair shakes hands exactly once?

(A) 12
(B) 22
(C) 66
(D) 132
(E) 244

_________________
CEO
Joined: 12 Sep 2015
Posts: 3848
Re: A group of 12 people who have never met are in a classroom. How many  [#permalink]

### Show Tags

03 Jan 2019, 09:38
4
Top Contributor
Bunuel wrote:
A group of 12 people who have never met are in a classroom. How many handshakes are exchanged if each pair shakes hands exactly once?

(A) 12
(B) 22
(C) 66
(D) 132
(E) 244

Here's an approach that doesn't require any counting techniques:

Since a person cannot shake hands with himself/herself, each person shakes hands with exactly 11 other people
So, we have 12 people and each experiences 11 handshakes for a TOTAL of 132handshakes [since (12)(11) = 132]

IMPORTANT: at this point, we need to recognize that every handshake has been counted TWICE. For example, if Person A and Person B shake hands, then Person A counts it as a handshake, AND Person B also counts it as a handshake. Of course only one handshake occurred.

To account for the DUPLICATION, we'll divide 132 by 2 to get 66

Cheers,
Brent
_________________
Test confidently with gmatprepnow.com
Senior Manager
Joined: 28 Jul 2016
Posts: 469
Location: India
Concentration: Finance, Human Resources
GPA: 3.97
WE: Project Management (Investment Banking)
Re: A group of 12 people who have never met are in a classroom. How many  [#permalink]

### Show Tags

03 Jan 2019, 09:49
1
since each person will shake hands with the other person
so total handshakes = 12*11
however we have counted twice as only handshake is with other person
hence divide by 2
so (12*11)/2
general formula
n*(n-1)/2
=66
_________________
Please give Kudos. Kudos encourage active discussions and help the community grow
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 4242
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: A group of 12 people who have never met are in a classroom. How many  [#permalink]

### Show Tags

06 Jan 2019, 04:45
1
Bunuel wrote:
A group of 12 people who have never met are in a classroom. How many handshakes are exchanged if each pair shakes hands exactly once?

(A) 12
(B) 22
(C) 66
(D) 132
(E) 244

12c2;

12!/10!*2!
= 66

IMO C
_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.
Re: A group of 12 people who have never met are in a classroom. How many   [#permalink] 06 Jan 2019, 04:45
Display posts from previous: Sort by