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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] New post 01 Apr 2012, 03:15
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A
B
C
D
E

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Question Stats:

65% (02:04) correct 35% (00:41) wrong based on 124 sessions
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] New post 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.

Answer: D.
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Re: How many different handshakes are possible if six girls [#permalink] New post 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] New post 16 Jun 2014, 16:14
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Re: How many different handshakes are possible if six girls [#permalink] New post 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] New post 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.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: How many different handshakes are possible if six girls [#permalink] New post 17 Jun 2014, 21:35
Thanks Bunuel, your signature gives good links. thanks for that.
Re: How many different handshakes are possible if six girls   [#permalink] 17 Jun 2014, 21:35
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