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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: 5662
GMAT 1: 800 Q59 V59
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
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Difficulty:

15% (low)

Question Stats:

83% (00:47) correct 17% (01:26) wrong based on 65 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

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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 $99 for 3 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: 275 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: 231 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: 5952 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 _________________ Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372 Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html GMAT online Tutor Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 5662 GMAT 1: 800 Q59 V59 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$99 for 3 month Online Course"
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Re: In a certain conference, if all the n attendees shake hands 105 times,   [#permalink] 20 Aug 2017, 19:14
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