2024 AMC 12A Problem 1

Below is the professionally curated solution for Problem 1 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:whole number operations

Difficulty rating: 870

1.

What is the value of 99011019910101?9901\cdot101-99\cdot10101?

22

2020

2121

200200

20202020

Solution:

Directly, 9901101=990100+9901=10000019901\cdot101=990100+9901=1000001 and 9910101=101010010101=999999.99\cdot10101=1010100-10101=999999. Their difference is 1000001999999=2.1000001-999999=2. Thus, the correct answer is A.

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