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n number of people are attending a meeting. All of them shake hands ea

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n number of people are attending a meeting. All of them shake hands ea  [#permalink]

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New post 03 Oct 2017, 00:38
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A
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C
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E

Difficulty:

  35% (medium)

Question Stats:

68% (01:24) correct 32% (01:33) wrong based on 139 sessions

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[GMAT math practice question]

n number of people are attending a meeting. All of them shake hands each other. If all attendees shake hands 210 times, what is the value of n?

A. 15
B. 19
C. 20
D. 21
E. 25

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Re: n number of people are attending a meeting. All of them shake hands ea  [#permalink]

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New post 03 Oct 2017, 00:40
MathRevolution wrote:
[GMAT math practice question]

n number of people are attending a meeting. All of them shake hands each other. If all attendees shake hands 210 times, what is the value of n?

A. 15
B. 19
C. 20
D. 21
E. 25


This is the same questions as the following one with one number different: https://gmatclub.com/forum/in-a-certain ... 47397.html
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n number of people are attending a meeting. All of them shake hands ea  [#permalink]

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New post 05 Oct 2017, 02:16
=>

nC2 = n(n-1)/2 = 210
n(n-1) = 420
n(n-1) – 420 = 0
n^2 – n – 420 = 0
(n-21)(n+20) = 0
n = 21 or n = -21
n = 21 since n must be positive.

Answer: D
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n number of people are attending a meeting. All of them shake hands ea  [#permalink]

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New post 12 Sep 2018, 06:01
MathRevolution wrote:
[GMAT math practice question]

n number of people are attending a meeting. All of them shake hands each other. If all attendees shake hands 210 times, what is the value of n?

A. 15
B. 19
C. 20
D. 21
E. 25


\(\frac{n( n - 1 )}{2} = 210\) ( As each person shakes hand with everyone except his own )

Now, \(n( n - 1 ) = 420\)

Or, \(n( n - 1 ) = 21*20\)

So, \(n = 20\), Answer must be (C)

stne - Needful done.
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Re: n number of people are attending a meeting. All of them shake hands ea  [#permalink]

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New post 14 Sep 2018, 08:04
MathRevolution wrote:
[GMAT math practice question]

n number of people are attending a meeting. All of them shake hands each other. If all attendees shake hands 210 times, what is the value of n?

A. 15
B. 19
C. 20
D. 21
E. 25


We have nC2 = 210:

n!/(2! x (n - 2)! = 210

n(n - 1)(n - 2)!/[2! x (n - 2)!] = 210

n(n - 1)/2! = 210

n^2 - n = 420

n^2 - n - 420 = 0

(n - 21)(n + 20) = 0

n = 21

Answer: D
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Re: n number of people are attending a meeting. All of them shake hands ea  [#permalink]

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New post 13 Oct 2018, 02:42
With back solving method, one can get to the answer in 30 seconds.

Started with C

20c2 = 20x19/2x1 = 190

21c2 = 21x20/2x1 = 210

Hence D
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Re: n number of people are attending a meeting. All of them shake hands ea   [#permalink] 13 Oct 2018, 02:42
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