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How many guests were present at the party?

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Manager
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Joined: 18 Jan 2017
Posts: 84
Location: India
Concentration: Finance, Economics
GMAT 1: 700 Q50 V34
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How many guests were present at the party?  [#permalink]

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New post 24 Jun 2017, 19:31
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  15% (low)

Question Stats:

76% (00:52) correct 24% (01:05) wrong based on 173 sessions

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How many guests were present at the party?

1)There were 45 handshakes if the guests shook hands with each other and every 2 guests shook hands exactly once
2)If there were half as many guests present, they could sit in a row in 120 different ways
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Joined: 05 Mar 2015
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How many guests were present at the party?  [#permalink]

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New post 24 Jun 2017, 19:54
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Tan2017 wrote:
How many guests were present at the party?

1)There were 45 handshakes if the guests shook hands with each other and every 2 guests shook hands exactly once
2)If there were half as many guests present, they could sit in a row in 120 different ways



(1) n*(n-1)/2 =45-------(since total handshakes in nC2 ways)

n(n-1) = 90
n=10
suff..

(2) half guests in 120 ways = 5!
thus half guests were =5 members
total (full) = 2*5= 10
suff

Ans D
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How many guests were present at the party?  [#permalink]

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New post 14 Aug 2017, 11:43
Tan2017 wrote:
How many guests were present at the party?

1)There were 45 handshakes if the guests shook hands with each other and every 2 guests shook hands exactly once
2)If there were half as many guests present, they could sit in a row in 120 different ways


let n be the number of guests

Stmt 1- the number of handshakes between the guests could be obtained by nC2 where we need to select 2 guests for a shake.

nC2=45. Sufficient to calculate n.

Stmt 2- (n/2) guests could be seated in a row in (n/2)! ways. Given, (n/2)! = 120. Sufficient to calculate n.

Ans D.
How many guests were present at the party? &nbs [#permalink] 14 Aug 2017, 11:43
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