Question

In an All-Area track meet, $216$ sprinters enter a $100$ -meter dash competition. The track has $6$ lanes, so only $6$ sprinters can compete at a time. At the end of each race, the five non-winners are eliminated, and the winner will compete again in a later race.

How many races are needed to determine the champion sprinter?

$36$

$42$

$43$

$60$

$72$

Answer: C

Concepts:basic counting

Difficulty rating: 1170

Video solution:

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Written solution:

Note that each race eliminates $5$ people. For there to be a winner, $215$ must be eliminated. Therefore, $215 / 5 = 43$ races are required to eliminate this number of people.

Thus, C is the correct answer.

2016 AMC 8 Problem 18

Answer: C

Difficulty rating: 1170

Video solution:

Written solution:

Problem 18 in Other Years