Question

There are $100$ players in a singles tennis tournament. The tournament is single elimination, meaning that a player who loses a match is eliminated. In the first round, the strongest $28$ players are given a bye, and the remaining $72$ players are paired off to play. After each round, the remaining players play in the next round. The match continues until only one player remains unbeaten. The total number of matches played is

a prime number

divisible by $2$

divisible by $5$

divisible by $7$

divisible by $11$

Answer: E

Concepts:basic counting invariant

Difficulty rating: 1280

Solution:

Each match eliminates exactly one player. Since $100$ players start and all but the champion are eliminated, there are $99$ matches.

Because $99=9 \cdot 11,$ it is divisible by $11$ but satisfies none of the other options.

Thus, the correct answer is E.

2003 AMC 10B Problem 15

Answer: E

Difficulty rating: 1280

Solution:

Problem 15 in Other Years