On the occasion of a certain meeting each member shake hand to the remaining…
2023
On the occasion of a certain meeting each member shake hand to the remaining number . If the total shake were 1176 , how many members were present for the meeting ?
- A.
48
- B.
58
- C.
49
- D.
59
Attempted by 5 students.
Show answer & explanation
Correct answer: C
Let n be the number of people. Each pair of people shakes hands once, so the total number of handshakes is n(n-1)/2.
Set up the equation: n(n-1)/2 = 1176. Multiply both sides by 2 to get n^2 - n - 2352 = 0.
Solve the quadratic using the discriminant: D = (-1)^2 - 4·1·(-2352) = 1 + 9408 = 9409, and sqrt(D) = 97.
Thus n = (1 + 97)/2 = 49 (the negative root is rejected because n must be positive).
Answer: 49
Check: 49×48/2 = 1176, which matches the given total.