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# 2). In a class comprising boys and girls, there were 45 hand

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Manager
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2). In a class comprising boys and girls, there were 45 hand [#permalink]

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16 May 2008, 08:04
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2). In a class comprising boys and girls, there were 45 hand shakes amongst the girls and 105 hand shakes amongst the boys. How many hand shakes took place between a boy and a girl, if each member of the class shook hands exactly once with every other student in the class?
A) 25
B) 15
C) 150
D) 300
E) 24
Current Student
Joined: 28 Dec 2004
Posts: 3363
Location: New York City
Schools: Wharton'11 HBS'12
Followers: 15

Kudos [?]: 297 [0], given: 2

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16 May 2008, 08:29
wizardofwashington wrote:
2). In a class comprising boys and girls, there were 45 hand shakes amongst the girls and 105 hand shakes amongst the boys. How many hand shakes took place between a boy and a girl, if each member of the class shook hands exactly once with every other student in the class?
A) 25
B) 15
C) 150
D) 300
E) 24

45 hand shakes amongst girls..=N(N+1)=90..N=9.well it should be 9+1 since its inclusive..10

105 handshakes=N(N+1)=210 N=14..well again it should be 15 since its inclusive..

15*10=150 handshakes amongst girls and boys..
Manager
Joined: 04 Sep 2007
Posts: 215
Followers: 1

Kudos [?]: 17 [0], given: 0

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16 May 2008, 08:48
fresinha12 wrote:
wizardofwashington wrote:
2). In a class comprising boys and girls, there were 45 hand shakes amongst the girls and 105 hand shakes amongst the boys. How many hand shakes took place between a boy and a girl, if each member of the class shook hands exactly once with every other student in the class?
A) 25
B) 15
C) 150
D) 300
E) 24

45 hand shakes amongst girls..=N(N+1)=90..N=9.well it should be 9+1 since its inclusive..10

105 handshakes=N(N+1)=210 N=14..well again it should be 15 since its inclusive..

15*10=150 handshakes amongst girls and boys..

This is probably a dumb question but I am having a hard time trying to figure out how you were able to Decode 45 handshakes to 10 Girls? The formulae N (N+1) sounds familiar but I am not able to recollect where I came across this one. Could you please offer me a reference source for me to get familiar with this concept? Thanks much.
Current Student
Joined: 28 Dec 2004
Posts: 3363
Location: New York City
Schools: Wharton'11 HBS'12
Followers: 15

Kudos [?]: 297 [0], given: 2

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16 May 2008, 08:53
wizardofwashington wrote:
fresinha12 wrote:
wizardofwashington wrote:
2). In a class comprising boys and girls, there were 45 hand shakes amongst the girls and 105 hand shakes amongst the boys. How many hand shakes took place between a boy and a girl, if each member of the class shook hands exactly once with every other student in the class?
A) 25
B) 15
C) 150
D) 300
E) 24

45 hand shakes amongst girls..=N(N+1)=90..N=9.well it should be 9+1 since its inclusive..10

105 handshakes=N(N+1)=210 N=14..well again it should be 15 since its inclusive..

15*10=150 handshakes amongst girls and boys..

This is probably a dumb question but I am having a hard time trying to figure out how you were able to Decode 45 handshakes to 10 Girls? The formulae N (N=1) sounds familiar but I am not able to recollect where I came across this one. Could you please offer me a reference source for me to get familiar with this concept? Thanks much.

yes you can use N*N-1 well actually thats really what i was using..

the question says NC2=45.. N*N-1=90.. we are told that amongst the girl there are 45 hand shakes..remember it takes 2 girls to handshake 1 time..so we are really looking to know how many ways can i choose 2 girls out of N...such that the number of ways=45..

hope this helps!

the way i tried to solve the problem was through logic..but obviously if you know the concept of NchooseX..then by all means..make your life easier
Manager
Joined: 04 Sep 2007
Posts: 215
Followers: 1

Kudos [?]: 17 [0], given: 0

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16 May 2008, 09:03
Re: PS - Handshakes   [#permalink] 16 May 2008, 09:03
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