How many different handshakes are possible if six girls : GMAT Problem Solving (PS)
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# How many different handshakes are possible if six girls

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

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01 Apr 2012, 03:15
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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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Re: How many different handshakes are possible if six girls [#permalink]

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01 Apr 2012, 03:27
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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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Re: How many different handshakes are possible if six girls [#permalink]

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24 Dec 2012, 00:39
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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, 16:14
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Re: How many different handshakes are possible if six girls [#permalink]

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17 Jun 2014, 06:27
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, 06:43
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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, 21:35
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Re: How many different handshakes are possible if six girls [#permalink]

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19 Nov 2014, 09:05
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, 06:39
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, 06:38
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How many different handshakes are possible if six girls [#permalink]

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04 Mar 2016, 18:18
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
How many different handshakes are possible if six girls   [#permalink] 04 Mar 2016, 18:18
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