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# How many different handshakes are possible if six girls

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Manager
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How many different handshakes are possible if six girls [#permalink]

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01 Apr 2012, 04:15
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Difficulty:

55% (hard)

Question Stats:

61% (01:08) correct 39% (01:15) wrong based on 403 sessions

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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?
[Reveal] Spoiler: OA

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Math Expert
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Re: How many different handshakes are possible if six girls [#permalink]

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01 Apr 2012, 04:27
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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.

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Manager
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Re: How many different handshakes are possible if six girls [#permalink]

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24 Dec 2012, 01:39
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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...
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Re: How many different handshakes are possible if six girls [#permalink]

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16 Jun 2014, 17:14
Hello from the GMAT Club BumpBot!

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Re: How many different handshakes are possible if six girls [#permalink]

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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

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Re: How many different handshakes are possible if six girls [#permalink]

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17 Jun 2014, 07:43
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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.
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Re: How many different handshakes are possible if six girls [#permalink]

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17 Jun 2014, 22:35

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Re: How many different handshakes are possible if six girls [#permalink]

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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]

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Re: How many different handshakes are possible if six girls [#permalink]

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20 Nov 2014, 07:39
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...

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Re: How many different handshakes are possible if six girls [#permalink]

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04 Mar 2016, 07:38
Hello from the GMAT Club BumpBot!

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How many different handshakes are possible if six girls [#permalink]

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04 Mar 2016, 19:18
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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

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Re: How many different handshakes are possible if six girls [#permalink]

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16 Mar 2017, 18:00
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: How many different handshakes are possible if six girls [#permalink]

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17 Mar 2017, 01:52
this case is similar to find the number of diagonals = 6C1 x 3C1/2 = 9. ANSWER

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Re: How many different handshakes are possible if six girls [#permalink]

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13 Aug 2017, 01:20
Don't know whether I'm right, or wrong, but I solved this this way: 6C2 - 4C2.

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Re: How many different handshakes are possible if six girls [#permalink]

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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!

Kudos [?]: 21 [0], given: 618

Re: How many different handshakes are possible if six girls   [#permalink] 18 Aug 2017, 23:33
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