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2007 AMC 10B Problem 2

Problem 2 of 25EasierAlgebra

Define the operation ⋆\star by a⋆b=(a+b)b.a\star b = (a+b)b. What is (3⋆5)−(5⋆3)?(3\star 5)-(5\star 3)?

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Solution

Since 3⋆5=(3+5)⋅5=403\star 5=(3+5)\cdot 5=40 and 5⋆3=(5+3)⋅3=24,5\star 3=(5+3)\cdot 3=24, the difference is 40−24=16.40-24=16. Thus, the correct answer is E.

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Concepts: custom operation · order of operations

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