2024 AMC 12A Problem 3

Below is the professionally curated solution for Problem 3 of the 2024 AMC 12A, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2024 AMC 12A solutions, or check the answer key.

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Concepts:optimizationbounding to limit cases

Difficulty rating: 1100

3.

The number 20242024 is written as the sum of not necessarily distinct two-digit numbers. What is the least number of two-digit numbers needed to write this sum?

2020

2121

2222

2323

2424

Solution:

Each number is at most 99,99, so kk numbers sum to at most 99k.99k. Since 9920=1980<2024,99\cdot20=1980\lt2024, at least 2121 numbers are required. With 21,21, we can use twenty 9999s and one 4444: 2099+44=1980+44=2024.20\cdot99+44=1980+44=2024. Thus, the correct answer is B.

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