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

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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n number of people are attending a meeting. All of them shake hands ea  [#permalink]

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03 Oct 2017, 01:38
00:00

Difficulty:

35% (medium)

Question Stats:

68% (01:24) correct 32% (01:34) wrong based on 146 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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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Math Expert Joined: 02 Sep 2009 Posts: 58381 Re: n number of people are attending a meeting. All of them shake hands ea [#permalink] ### Show Tags 03 Oct 2017, 01:40 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 _________________ Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8011 GMAT 1: 760 Q51 V42 GPA: 3.82 n number of people are attending a meeting. All of them shake hands ea [#permalink] ### Show Tags 05 Oct 2017, 03:16 => 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 _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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n number of people are attending a meeting. All of them shake hands ea  [#permalink]

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12 Sep 2018, 07:01
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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14 Sep 2018, 09:04
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

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

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13 Oct 2018, 03:42
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
Re: n number of people are attending a meeting. All of them shake hands ea   [#permalink] 13 Oct 2018, 03:42
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