GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 25 Sep 2018, 22:24

### 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

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

Author Message
TAGS:

### Hide Tags

Manager
Joined: 10 Feb 2011
Posts: 109
If 10 persons meet at a reunion and each person shakes hands  [#permalink]

### Show Tags

09 Mar 2011, 15:12
6
00:00

Difficulty:

5% (low)

Question Stats:

74% (00:43) correct 26% (00:51) wrong based on 457 sessions

### HideShow timer Statistics

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
Math Expert
Joined: 02 Sep 2009
Posts: 49493
Re: . If 10 persons meet at a reunion and each person shakes han  [#permalink]

### Show Tags

09 Mar 2011, 15:20
2
1
banksy 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

The total # of handshakes will be equal to the # of different pairs possible from these 10 people (one handshake per pair), so $$C^2_{10}=45$$.

_________________
Intern
Status: Going the extra mile
Joined: 08 Feb 2014
Posts: 18
Location: Netherlands
GMAT 1: 470 Q37 V18
GMAT 2: 570 Q36 V32
GMAT 3: 560 Q37 V30
GMAT 4: 610 Q41 V34
Re: If 10 persons meet at a reunion and each person shakes hands  [#permalink]

### Show Tags

29 Apr 2014, 12:17
1
We got #10 people who shake each other's hands once ==> a pair of 2

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

_________________

Structural persistence is the key to succes .
Party hard, study harder.

Still bashing, will continue to do so , although it's important to chill aswell ; )
STUDY+CHILL=VICTORY

SVP
Joined: 06 Nov 2014
Posts: 1886
Re: If 10 persons meet at a reunion and each person shakes hands  [#permalink]

### Show Tags

16 Sep 2015, 21:03
Handshakes are made in a pair of 2
Hence the total handshakes = total different different pairs

This can be found by 10C2= 10!/8!*2!

On solving , we get 45 (Option D)
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12459
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If 10 persons meet at a reunion and each person shakes hands  [#permalink]

### Show Tags

20 Mar 2018, 11:46
1
Hi All,

This question can be solved in a couple of ways: a high-concept math approach or a "brute-force" answer that anyone can use. I'll focus on the second method.

Since we have 10 people, who will all shake hands with one another, we know that each pair of people will lead to 1 hand shake (and a person CAN'T shake hands with himself or herself).

If we call the people ABCDE FGHIJ

Person A will shake hands with BCDE FGHIJ = 9 shakes

Person B ALREADY shook hands with A, so they won't shake hands again….
Person B will shake hands with CDE FGHIJ = 8 shakes

Person C ALREADY shook hands with A and B, so they won't shake hands again….
Person C will shake hands with DE FGHIJ = 7 shakes

Notice the pattern 9, 8, 7…..the numbers will shrink by 1 with every letter, so we'll end up with…

9+8+7+6+5+4+3+2+1+0 = 45 total handshakes.

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

Re: If 10 persons meet at a reunion and each person shakes hands &nbs [#permalink] 20 Mar 2018, 11:46
Display posts from previous: Sort by

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

## Events & Promotions

 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®.