2024 AMC 10B Problem 1

Below is the professionally curated solution for Problem 1 of the 2024 AMC 10B, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2024 AMC 10B solutions, or check the answer key.

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Concepts:basic counting

Difficulty rating: 860

In a long line of people, the $1013$ th person from the left is also the $1010$ th person from the right. How many people are in the line?

$2021$

$2022$

$2023$

$2024$

$2025$

Solution:

There are $1012$ people to the left of this spot and $1009$ to the right. Add those two groups plus the person themselves: $1012 + 1009 + 1 = 2022.$ Or, just as fast, the two positions overlap on one person, so $1013 + 1010 - 1 = 2022.$ Thus, B is the correct answer.

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Problem 1 in Other Years

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