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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## Permutations and Combination tagged by: BTGmoderatorRO ##### This topic has 2 expert replies and 0 member replies ## Permutations and Combination Everyone shakes hands with everyone else in a room. Total number of handshakes is 66. Number of persons a. 14 b. 12 c. 11 d. 15 e. 16 OA is B What is the Mathematical approach to solving this question? ### GMAT/MBA Expert Legendary Member Joined 14 Jan 2015 Posted: 2667 messages Followed by: 122 members Upvotes: 1153 GMAT Score: 770 Roland2rule wrote: Everyone shakes hands with everyone else in a room. Total number of handshakes is 66. Number of persons a. 14 b. 12 c. 11 d. 15 e. 16 OA is B What is the Mathematical approach to solving this question? Use the answer choices. Test 'C.' Say there were 11 people in the room. There'd be 10 people left for each of those people to shake hands with. But bear in mind that when Dave shakes hands with Roland, it's not a different scenario than Roland shakes hands with Dave. So we need to divide by 2! to account for the fact that those people are interchangeable once we select them. So 11*10/2! = We want 66. But notice we're close. Test B. If there are 12 people, there are 11 people left to shake with. And we need to divide by 2! to account for the fact that the people are interchangeable. 12*11/2! = 66. So we're done. B is the answer _________________ Veritas Prep | GMAT Instructor Veritas Prep Reviews Save$100 off any live Veritas Prep GMAT Course

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Roland2rule wrote:
Everyone shakes hands with everyone else in a room. Total number of handshakes is 66. Number of persons

a. 14
b. 12
c. 11
d. 15
e. 16

OA is B

What is the Mathematical approach to solving this question?
And if you're a fiend for algebra, if we say there are 'x' people in the room, there will be (x-1) people for each to shake hands with. Because the two people engaged in a shake are interchangeable, we need to divide by 2!.

So x*(x-1)/2! = 66
x*(x-1) = 132
x^2 - x - 132 = 0
(x-12)(x+11) = 0
x = 12 or x = -11. We can't have negative people, so x=12. The answer is B

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