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# If 10 persons meet at a reunion and each person shakes hands

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Manager
Joined: 05 Sep 2007
Posts: 144
Location: New York
If 10 persons meet at a reunion and each person shakes hands  [#permalink]

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31 Mar 2008, 18:19
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Question Stats:

100% (00:42) correct 0% (00:00) wrong based on 0 sessions

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If 10 persons meet at a reunion and each person shakes hands exactly once with each of the others, what is the total number of handshakes?
(A) 10•9•8•7•6•5•4•3•2•1
(B) 10•10
(C) 10•9
(D) 45
(E) 36

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Director
Joined: 10 Sep 2007
Posts: 909

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31 Mar 2008, 18:32
People shaking hands are expressed by = n(n-1)/2
As there are 10 people so = 10*9/2 = 45

Senior Manager
Joined: 01 Feb 2005
Posts: 262

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31 Mar 2008, 18:44
45

First person shakes hands with 9 people
2nd person shakes hands with 8 people
and so on.... all the way to 1

Add the sum = 45 (D) 45
Manager
Joined: 14 Jun 2007
Posts: 158
Location: Vienna, Austria

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20 Oct 2008, 01:38
guys
can someone tell me why: n(n-1)/2 is used to get the number of handshakes?

isn´t that a modification of the sum formula n*(n+1)/2 ?

thanks for clarification
VP
Joined: 17 Jun 2008
Posts: 1474

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20 Oct 2008, 05:35
domleon wrote:
guys
can someone tell me why: n(n-1)/2 is used to get the number of handshakes?

isn´t that a modification of the sum formula n*(n+1)/2 ?

thanks for clarification

More than the formula, I will go by actual numbers to be added. Since, it is 9+8+7+....+1 hence, sum = 9*10/2.
VP
Joined: 30 Jun 2008
Posts: 1004

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20 Oct 2008, 05:57
scthakur wrote:

More than the formula, I will go by actual numbers to be added. Since, it is 9+8+7+....+1 hence, sum = 9*10/2.

Why do we add here ? why not multiplication? 9*8*7.....
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Current Student
Joined: 28 Dec 2004
Posts: 3280
Location: New York City
Schools: Wharton'11 HBS'12

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20 Oct 2008, 07:58
i am not a big fan formulas...but its good to understand them...

lets see..what is the total number of hand shakes..well its N*(N-1) number of total possibilites..but keep in mind it takes 2 people to shake hands as such..the total number of handshakes will be n*(n-1)/2

10*9/2=45
VP
Joined: 17 Jun 2008
Posts: 1474

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20 Oct 2008, 11:12
amitdgr wrote:
scthakur wrote:

More than the formula, I will go by actual numbers to be added. Since, it is 9+8+7+....+1 hence, sum = 9*10/2.

Why do we add here ? why not multiplication? 9*8*7.....

It is because, each person shakes hand only once.
VP
Joined: 17 Jun 2008
Posts: 1279

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20 Oct 2008, 13:45
el1981 wrote:
If 10 persons meet at a reunion and each person shakes hands exactly once with each of the others, what is the total number of handshakes?
(A) 10•9•8•7•6•5•4•3•2•1
(B) 10•10
(C) 10•9
(D) 45
(E) 36

selecting pair of people from 10 : 10C2 =10*9/2 =45

IMO D
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VP
Joined: 05 Jul 2008
Posts: 1329

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21 Oct 2008, 20:17
amitdgr wrote:
scthakur wrote:

More than the formula, I will go by actual numbers to be added. Since, it is 9+8+7+....+1 hence, sum = 9*10/2.

Why do we add here ? why not multiplication? 9*8*7.....

We don't multiply because we are enumerating the number of hand shakes A can possibly do, B can do and so on on until J, if there are A to J people.
VP
Joined: 30 Jun 2008
Posts: 1004

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21 Oct 2008, 21:04
icandy wrote:
amitdgr wrote:
scthakur wrote:

More than the formula, I will go by actual numbers to be added. Since, it is 9+8+7+....+1 hence, sum = 9*10/2.

Why do we add here ? why not multiplication? 9*8*7.....

We don't multiply because we are enumerating the number of hand shakes A can possibly do, B can do and so on on until J, if there are A to J people.

thanks icandy ... i sort of get it now

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

_________________

"You have to find it. No one else can find it for you." - Bjorn Borg

Re: PS: handshake &nbs [#permalink] 21 Oct 2008, 21:04
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