In a birthday party, every person shakes hand with every other person. If…
2025
In a birthday party, every person shakes hand with every other person. If there were a total of 28 handshakes in the party, how many persons were present?
- A.
8
- B.
9
- C.
6
- D.
7
Attempted by 37 students.
Show answer & explanation
Correct answer: A
Key formula: Number of handshakes = n(n − 1)/2, where n is the number of people.
Set up the equation using the given total: n(n − 1)/2 = 28. Multiply both sides by 2 to get n(n − 1) = 56.
Observe that 56 = 7 × 8, and 7 and 8 are consecutive integers, so n = 8.
Alternative check using the quadratic: n^2 − n − 56 = 0. Solve using the quadratic formula: n = (1 ± sqrt(1 + 224))/2 = (1 ± 15)/2. The positive solution is n = (1 + 15)/2 = 8.
Therefore, the number of persons present is 8.