AMC 10A 2026 (Problem 13)
Two bicycle clubs, with disjoint memberships, go on a tour together. On the morning of the tour, members greet each other with a handshake. Everyone shakes hands with everyone else exactly once. There were 119 handshakes between members of the same club and 112 handshakes between members of different clubs. How many more people came from the larger club than from the smaller club?
Let and be the numbers of people in Clubs 1 and 2, respectively.
There were 119 handshakes between members of the same club, so
There were 119 handshakes between members of the same club, so
There were 112 handshakes between members of different clubs, so
By Hints 2 and 3,
(C) 6