Art of Problem Solving

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AMC 12C 2020

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Problem 1

What is the sum of the solutions to the equation $(x + 5)(x + 4) - (x + 5)(x - 6) = 100$ ?

Problem 2

How many increasing subsets of ${{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}}$ contain no $2$ consecutive prime numbers?

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