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romitvsingh: Senior | Next Rank: 100 Posts; Posts: 46; Joined: Fri Aug 19, 2011 12:13 am; Location: Delhi, India; Followed by:1 members

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by romitvsingh » Mon Oct 31, 2011 8:26 pm

Everyone shakes hands with everyone else in a room. Total number of handshakes is 66. Number of persons=?

Possible AnswersSelected Possible Answer
A. 14

B. 13

C. 11

D. 12

E. 10

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Source: Beat The GMAT — Problem Solving | Mon Oct 31, 2011 8:26 pm

GmatMathPro: GMAT Instructor; Posts: 349; Joined: Wed Sep 28, 2011 3:38 pm; Location: Austin, TX; Thanked: 236 times; Followed by:54 members; GMAT Score:770

by GmatMathPro » Mon Oct 31, 2011 8:34 pm

It takes two people to perform one handshake, so the number of handshakes is the same as the number of ways to choose 2 people from the room. To choose 2 people out of a room full of n people, you have n choices for the first person, and n-1 choices for the 2nd person. That's n*(n-1) pairs, but we have to divide by 2 to prevent double counting the handshakes (we don't want to count X shaking hands with Y AND Y shaking hands with X). So, n(n-1)/2=66. Solve for n=12.

Ans: D. 12

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rijul007: Legendary Member; Posts: 588; Joined: Sun Oct 16, 2011 9:42 am; Location: New Delhi, India; Thanked: 130 times; Followed by:9 members; GMAT Score:720

by rijul007 » Mon Oct 31, 2011 8:51 pm

nC2 =66

n=12

Option D

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vaibhavgupta: Master | Next Rank: 500 Posts; Posts: 416; Joined: Tue Aug 30, 2011 2:18 pm; Location: Delhi, India; Thanked: 13 times; Followed by:9 members

by vaibhavgupta » Wed Nov 02, 2011 2:15 pm

romitvsingh wrote:Everyone shakes hands with everyone else in a room. Total number of handshakes is 66. Number of persons=?

Possible AnswersSelected Possible Answer
A. 14

B. 13

C. 11

D. 12

E. 10