2024 AMC 12B Problem 1

Below is the professionally curated solution for Problem 1 of the 2024 AMC 12B, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2024 AMC 12B solutions, or check the answer key.

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Concepts:counting integers in a rangebasic counting

Difficulty rating: 890

1.

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

20212021

20222022

20232023

20242024

20252025

Solution:

The target person has 10131=10121013 - 1 = 1012 people to the left and 10101=10091010 - 1 = 1009 people to the right. Including the person themself, the line has 1012+1009+1=20221012 + 1009 + 1 = 2022 people.

Thus, the correct answer is B.

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