2024 AMC 12A Problem 1

Attempt Problem 1 of the 2024 AMC 12A below, then check your answer against the professionally curated solution 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.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

1.

What is the value of 9901⋅101−99⋅10101?9901\cdot101-99\cdot10101?
22
2020
2121
200200
20202020
Answer: A
Concepts:whole number operations
Small hint:
9901⋅101=9901⋅100+99019901\cdot101=9901\cdot100+9901
Big hint:
99⋅10101=100⋅10101−1010199\cdot10101=100\cdot10101-10101
Solution:
Directly, 9901⋅101=9901009901\cdot101=990100 +9901=1000001+9901=1000001 and 99⋅10101=101010099\cdot10101=1010100 −10101=999999.-10101=999999. Their difference is 1000001−999999=2.1000001-999999=2. Thus, the correct answer is A.
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