2004 · Q79
79. At the conclusion of a party, a total number of 28 handshakes was exchanged. Every person in the party shook hands with every other person who attended the party. What was the total number of persons who attended the party?
MathematicsCombinatorics
- A8
- B14
- C28
- D56
Explanation
If n persons each shake hands with every other person, the number of handshakes is n(n−1)/2 = 28. Solving n² − n − 56 = 0 gives (n−8)(n+7) = 0, so n = 8 persons attended.