NEW HERE? LEARN MORE
closeclose
It is currently 19 Apr 2024, 13:40
Register
GMAT Focus Tests
Decision Tracker
My Rewards
New posts
New comers' posts

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

How many different handshakes are possible if six girls

18 posts Go to First Unread Post
Print view
NEW TOPIC
POST REPLY
Question banks

GMAT Question Banks

Downloads
My Bookmarks
Reviews
SORT BY:
Date
Kudos
User avatar
BN1989
Manager
Manager
Joined: 12 Oct 2011
Posts: 100
GMAT 1: 700 Q48 V37
GMAT 2: 720 Q48 V40
How many different handshakes are possible if six girls [#permalink] New post  01 Apr 2012, 04:15
2
Kudos
46
Bookmarks
00:00
A
B
C
D
E

Difficulty:

45% (medium)

Question Stats:

63% (01:34) correct 37% (01:44) wrong based on 813 sessions
Hide Show timer Statistics
How many different handshakes are possible if six girls are standing on a circle and each girl shakes hands with every other girl except the two girls standing next to her?

(A) 12
(B) 11
(C) 10
(D) 9
(E) 8

Had to count the scenarios, how can you calculte this with combinatorics?
ShowHide Answer
Official Answer
Official Answer and Stats are available only to registered users. Register/Login.
Most Helpful Reply
User avatar
eaakbari
Intern
Intern
Joined: 24 Mar 2010
Posts: 46
Re: How many different handshakes are possible if six girls [#permalink] New post  24 Dec 2012, 01:39
42
Kudos
5
Bookmarks
Well, I picked a weird way to do this but well it was a short approach

I thought of the girls as sides of a polygon, and a handshake as a diagonal.

Number of diagonal in a n-sided polygon is n(n-3)/2

Number of handshakes -> 6(3)/2 = 9

Hence D.


P.S.
Look what GMAT does to you, m picturing girls as "sides of a polygon"!!...Sigh...
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92760
CAT Tests Forum Quiz Mode
Re: How many different handshakes are possible if six girls [#permalink] New post  01 Apr 2012, 04:27
6
Kudos
16
Bookmarks
Expert Reply
BN1989 wrote:
How many different handshakes are possible if six girls are standing on a circle and each girl shakes hands with every other girl except the two girls standing next to her?

(A) 12
(B) 11
(C) 10
(D) 9
(E) 8

Had to count the scenarios, how can you calculte this with combinatorics?


Each girl in a circle shakes hands with 3 other girls (6 minus herself and the two girls standing next to her): 3*6=18, but since this number counts twice one handshake per pair then # handshakes possible is 18/2=9.

Answer: D.
_________________
New to the GMAT CLUB Forum?

My Signature Questions' Collection:


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics
Signature Read More
General Discussion
User avatar
GMatAspirerCA
Manager
Manager
Joined: 24 Oct 2012
Posts: 53
WE:Information Technology (Computer Software)
Re: How many different handshakes are possible if six girls [#permalink] New post  17 Jun 2014, 07:27
Hi
I am looking for some sample questions to test my arithmatic section, Can you tell me where are these questions from? where are these sub-600, 600 to 700 questions?
thanks
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92760
CAT Tests Forum Quiz Mode
Re: How many different handshakes are possible if six girls [#permalink] New post  17 Jun 2014, 07:43
1
Kudos
12
Bookmarks
Expert Reply
GMatAspirerCA wrote:
Hi
I am looking for some sample questions to test my arithmatic section, Can you tell me where are these questions from? where are these sub-600, 600 to 700 questions?
thanks


Check this first:

ALL YOU NEED FOR QUANT



Our questions banks: viewforumtags.php From there:
DS questions on Arithmetic: search.php?search_id=tag&tag_id=30
PS questions on Arithmetic: search.php?search_id=tag&tag_id=51

GMAT PS Question Directory by Topic & Difficulty: gmat-ps-question-directory-by-topic-difficulty-127957.html
GMAT DS Question Directory by Topic & Difficulty: ds-question-directory-by-topic-difficulty-128728.html

100 Hardest Data Sufficiency Questions: 100-hardest-data-sufficiency-questions-162413.html
100 Hardest Problem Solving Questions: 100-hardest-problem-solving-questions-162616.html

Hope this helps.
_________________
New to the GMAT CLUB Forum?

My Signature Questions' Collection:


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics
Signature Read More
User avatar
GMatAspirerCA
Manager
Manager
Joined: 24 Oct 2012
Posts: 53
WE:Information Technology (Computer Software)
Re: How many different handshakes are possible if six girls [#permalink] New post  17 Jun 2014, 22:35
Thanks Bunuel, your signature gives good links. thanks for that.
User avatar
vietnammba
Intern
Intern
Joined: 25 Jun 2014
Posts: 33
Re: How many different handshakes are possible if six girls [#permalink] New post  19 Nov 2014, 10:05
eaakbari wrote:
Well, I picked a weird way to do this but well it was a short approach

I thought of the girls as sides of a polygon, and a handshake as a diagonal.

Number of diagonal in a n-sided polygon is n(n-3)/2

Number of handshakes -> 6(3)/2 = 9

Hence D.


P.S.
Look what GMAT does to you, m picturing girls as "sides of a polygon"!!...Sigh...


I like ur approach and this is funny lol: Look what GMAT does to you, m picturing girls as "sides of a polygon"!!...Sigh...[/quote]
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92760
CAT Tests Forum Quiz Mode
Re: How many different handshakes are possible if six girls [#permalink] New post  20 Nov 2014, 07:39
Expert Reply
eaakbari wrote:
Well, I picked a weird way to do this but well it was a short approach

I thought of the girls as sides of a polygon, and a handshake as a diagonal.

Number of diagonal in a n-sided polygon is n(n-3)/2

Number of handshakes -> 6(3)/2 = 9

Hence D.


P.S.
Look what GMAT does to you, m picturing girls as "sides of a polygon"!!...Sigh...

________________

:-D :-D :-D
_________________
New to the GMAT CLUB Forum?

My Signature Questions' Collection:


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics
Signature Read More
User avatar
P
gracie
VP
VP
Joined: 07 Dec 2014
Posts: 1074
How many different handshakes are possible if six girls [#permalink] New post  04 Mar 2016, 19:18
1
Kudos
2
Bookmarks
let n=6
if each of the 6 girls shook hands with each of the other 5, there would be (n)(n-1)/2=15 total handshakes
because each of the 6 shakes hands with only 3 other girls, there are only (3/5)(15)=9 total handshakes
User avatar
S
KrishnakumarKA1
Senior Manager
Senior Manager
Joined: 05 Jan 2017
Posts: 416
Location: India
Re: How many different handshakes are possible if six girls [#permalink] New post  17 Mar 2017, 01:52
this case is similar to find the number of diagonals = 6C1 x 3C1/2 = 9. ANSWER
User avatar
B
lenric
Intern
Intern
Joined: 21 Sep 2016
Posts: 21
Re: How many different handshakes are possible if six girls [#permalink] New post  13 Aug 2017, 01:20
1
Kudos
Don't know whether I'm right, or wrong, but I solved this this way: 6C2 - 4C2.
User avatar
G
Madhavi1990
Senior Manager
Senior Manager
Joined: 15 Jan 2017
Posts: 259
Re: How many different handshakes are possible if six girls [#permalink] New post  18 Aug 2017, 23:33
eaakbari wrote:
Well, I picked a weird way to do this but well it was a short approach

I thought of the girls as sides of a polygon, and a handshake as a diagonal.

Number of diagonal in a n-sided polygon is n(n-3)/2

Number of handshakes -> 6(3)/2 = 9

Hence D.


P.S.
Look what GMAT does to you, m picturing girls as "sides of a polygon"!!...Sigh...



i will surely use this method for the circular/ 'standing in circle' and condition questions. Pretty insightful, thank you!
User avatar
P
100mitra
Director
Director
Joined: 29 Apr 2019
Status:Learning
Posts: 752
Re: How many different handshakes are possible if six girls [#permalink] New post  18 Sep 2021, 04:07
1
Kudos
Correct Answer - D - 9
Number of People - 6 (Condition : no hand shake with side member)

Method 1: Counting : (5+4+3+2+1) - (3+2+1) = 15 - 6= 9
Method 2 : Combinaton : 6C2 - 6C1 = 15 - 6 = 9
Method 3 : Mean : [(6x5)/2] - [(6*2)/2) = 15 - 6 = 9
Method 4 : Polygon approach : nC2-n = 6C2 - 6 = 15 - 6 = 9
avatar
sysysy9898
Intern
Intern
Joined: 02 Aug 2022
Posts: 1
Re: How many different handshakes are possible if six girls [#permalink] New post  02 Aug 2022, 06:25
Bunuel wrote:
BN1989 wrote:
How many different handshakes are possible if six girls are standing on a circle and each girl shakes hands with every other girl except the two girls standing next to her?

(A) 12
(B) 11
(C) 10
(D) 9
(E) 8

Had to count the scenarios, how can you calculte this with combinatorics?


Each girl in a circle shakes hands with 3 other girls (6 minus herself and the two girls standing next to her): 3*6=18, but since this number counts twice one handshake per pair then # handshakes possible is 18/2=9.

Answer: D.


i tried your method only 8 repeats came out from the 6 letters:
abcdef
a-def
b-def
c-def
d-abf (repeats: da db)
e-abc (repeats:ea eb ec)
f-abc (repeats:fa fb fc)

Bunuel
Which two letters am I missing?
because the answer to me seems to be 10
User avatar
G
ThatDudeKnows
Tutor
Joined: 11 May 2022
Posts: 1092
Re: How many different handshakes are possible if six girls [#permalink] New post  02 Aug 2022, 07:00
Expert Reply
sysysy9898 wrote:
Bunuel wrote:
BN1989 wrote:
How many different handshakes are possible if six girls are standing on a circle and each girl shakes hands with every other girl except the two girls standing next to her?

(A) 12
(B) 11
(C) 10
(D) 9
(E) 8

Had to count the scenarios, how can you calculte this with combinatorics?


Each girl in a circle shakes hands with 3 other girls (6 minus herself and the two girls standing next to her): 3*6=18, but since this number counts twice one handshake per pair then # handshakes possible is 18/2=9.

Answer: D.


i tried your method only 8 repeats came out from the 6 letters:
abcdef
a-def
b-def
c-def
d-abf (repeats: da db)
e-abc (repeats:ea eb ec)
f-abc (repeats:fa fb fc)

Bunuel
Which two letters am I missing?
because the answer to me seems to be 10


sysysy9898

You've got incorrect letters next to each of your starting ones. No girl can shake hands with the exact same three girls as any of the others, but you have a, b, and c, each shaking hands with d, e, and f. a can't shake with f and c can't shake with d. Here are the correct groupings using your methodology.

abcdef
a-cde
b-def
c-efa (repeats: ca)
d-fab (repeats: da db)
e-abc (repeats:ea eb ec)
f-bcd (repeats: fb fc fd)
User avatar
S
Paras96
Director
Director
Joined: 11 Sep 2022
Posts: 501
Location: India
Paras: Bhawsar
GMAT 1: 590 Q47 V24
GMAT 2: 580 Q49 V21
GMAT 3: 700 Q49 V35
GPA: 3.2
WE:Project Management (Other)
Re: How many different handshakes are possible if six girls [#permalink] New post  04 Sep 2023, 11:12
In a circle of 6 girls, each girl shakes hands with the 3 girls next to her (6 girls minus herself and the two girls on either side). This creates a total of 18 handshakes, but we need to remember that each handshake involves two individuals. So, to find the number of unique handshakes, we divide the total by 2.

Therefore, the correct number of unique handshakes among the 6 girls in the circle is 18 / 2 = 9.
User avatar
B
nissamis00
Intern
Intern
Joined: 24 Sep 2022
Posts: 5
CAT Tests
Re: How many different handshakes are possible if six girls [#permalink] New post  08 Sep 2023, 00:46
Look at the question closer

Its what the Number of diagonals of n sided polygon. Which in this case its n=6
so 6(6-3)/2 = 9
User avatar
L
KarishmaB
Tutor
Joined: 16 Oct 2010
Posts: 14815
Location: Pune, India
Re: How many different handshakes are possible if six girls [#permalink] New post  08 Sep 2023, 01:28
Expert Reply
BN1989 wrote:
How many different handshakes are possible if six girls are standing on a circle and each girl shakes hands with every other girl except the two girls standing next to her?

(A) 12
(B) 11
(C) 10
(D) 9
(E) 8

Had to count the scenarios, how can you calculte this with combinatorics?


Imagine each girl standing on the vertex of a hexagon. When one shakes hands with the girls next to her, they form a side. When she shakes hands with the girls away from her, they form a diagonal. So we need the number of diagonals that are present in a hexagon (since the girl must not shake hands with the girls next to her)
Number of diagonals in a hexagon = nC2 - n
Hence, Number of hand shakes here = 6C2 - 6 = 9

Check this post for a discussion on number of diagonals in a polygon: https://anaprep.com/geometry-diagonals- ... d-polygon/
GMAT Club Bot
gmatclubot
Re: How many different handshakes are possible if six girls [#permalink]
08 Sep 2023, 01:28
NEW TOPIC
POST REPLY
Downloads
My Bookmarks
Reviews
Moderators:
Bunuel
Math Expert
92760 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

cron

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions