RG - A Helping Hand (Company Secretary) (13867 Points)
24 August 2011
At a party, everyone shook hands with everybody else. There were 66 handshakes. How many people were at the party?
Mansi
(CA (Final), B.com)
(939 Points)
Replied 24 August 2011
I THINK AROUND 132 PEOPLE ARE THERE, BECAUSE ONE HANSHAKES NEED 2 PEOPLE
NOW U TELL THE ANSWER,
and if one person can shake hands more then 1 people then, answer will be different
REGARDS,
Mansi batra
RG - A Helping Hand
(Company Secretary)
(13867 Points)
Replied 24 August 2011
Thanks Mansi for reply. However it is not correct as per the answer with me.
Let's wait for some more replies...after that i'll share the answer.
RG
RG - A Helping Hand
(Company Secretary)
(13867 Points)
Replied 24 August 2011
Handshakes are used traditionally as greetings, but they are also used to seal an agreement when a business transaction has been mutually accepted. A handshake is sometimes used to characterize the personality of an individual. A firm handshake is interpreted to indicate an assertive person or an extroverted personality, whereas a less firm or limp handshake is viewed as a sign of weakness and lack of confidence. Some diseases, such as influenza, can be spread by shaking hands with an infected individual and then touching one's face. (See Hygiene)
With two people (A and B), there is one handshake
(A with B).
With three people (A, B, and C), there are three handshakes
(A with B and C; B with C).
With four people (A, B, C, and D), there are six handshakes
(A with B, C, and D; B with C and D; C with D).
In general, with n+1 people, the number of handshakes is the sum of the first n consecutive numbers: 1+2+3+ ... + n.
Since this sum is n(n+1)/2, we need to solve the equation n(n+1)/2 = 66.
This is the quadratic equation n2+ n -132 = 0. Solving for n, we obtain 11 as the answer and deduce that there were 12 people at the party.
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