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# In a certain conference, if all the n attendees shake hands 105 times,

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8011
GMAT 1: 760 Q51 V42
GPA: 3.82
In a certain conference, if all the n attendees shake hands 105 times,  [#permalink]

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18 Aug 2017, 01:56
00:00

Difficulty:

25% (medium)

Question Stats:

76% (01:31) correct 24% (01:22) wrong based on 142 sessions

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In a certain conference, if all the n attendees shake hands 105 times, what is the value of n?

A. 10
B. 12
C. 15
D. 16
E. 18

_________________
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" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Senior Manager Joined: 19 Apr 2016 Posts: 269 Location: India GMAT 1: 570 Q48 V22 GMAT 2: 640 Q49 V28 GPA: 3.5 WE: Web Development (Computer Software) Re: In a certain conference, if all the n attendees shake hands 105 times, [#permalink] ### Show Tags 18 Aug 2017, 02:01 1 MathRevolution wrote: In a certain conference, if all the n attendees shake hands 105 times, what is the value of n? A. 10 B. 12 C. 15 D. 16 E. 18 n(n-1)/2 = 105 n(n-1) = 210 (n-15)(n+14) = 210 n = 15 Hence option C is correct Hit Kudos if you liked it 8-) Manager Joined: 27 Dec 2016 Posts: 227 Concentration: Marketing, Social Entrepreneurship GPA: 3.65 WE: Marketing (Education) Re: In a certain conference, if all the n attendees shake hands 105 times, [#permalink] ### Show Tags 18 Aug 2017, 04:39 I solved this question in 1,5 minutes, but with plug in method. Since this one is a combination problem, so we should determine what nCr will have 105 in result. MathRevolution, do we have more straightforward approach? _________________ There's an app for that - Steve Jobs. Math Expert Joined: 02 Aug 2009 Posts: 7961 Re: In a certain conference, if all the n attendees shake hands 105 times, [#permalink] ### Show Tags 18 Aug 2017, 05:02 MathRevolution wrote: In a certain conference, if all the n attendees shake hands 105 times, what is the value of n? A. 10 B. 12 C. 15 D. 16 E. 18 Hi.. Ofcourse the Q should mention that each shake hands with others once. So choosing 2 out of n is nC2=$$\frac{n!}{(n-2)!2!}=\frac{n*(n-1)*(n-2)!}{(n-2)!*2!}=\frac{n*(n-1)}{2}=105....$$... $$n(n-1)=210=2*3*5*7=3*5*2*7=15*14$$ So n is 15 C _________________ Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8011 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: In a certain conference, if all the n attendees shake hands 105 times, [#permalink] ### Show Tags 20 Aug 2017, 19:14 nC2 = 105. n(n-1)/(1*2) = 105 n(n-1) = 210 n(n-1) = 15*14 Thus n = 15. Ans: C _________________ 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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Re: In a certain conference, if all the n attendees shake hands 105 times,  [#permalink]

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13 Oct 2018, 04:28
MathRevolution wrote:
In a certain conference, if all the n attendees shake hands 105 times, what is the value of n?

A. 10
B. 12
C. 15
D. 16
E. 18

Backsolving

Nc2 = (n)(n-1)/2

Pick a number and try.

(15 * 14)/2 = 15 * 7 = 105.

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Re: In a certain conference, if all the n attendees shake hands 105 times,   [#permalink] 13 Oct 2018, 04:28
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