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2024 AMC 12A Problem 1

Problem 1 of 25EasierAlgebra

What is the value of 9901⋅101−99⋅10101?9901\cdot101-99\cdot10101?

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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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Concepts: whole number operations

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.