# 2015 Mock AIME I Problem 1: Picking Numbers from a Hat

Algebra Level 2

David, Justin, Richard, and Palmer are demonstrating a "math magic'' concept in front of an audience. There are four boxes, labeled A, B, C, and D, and each one contains a different number. First, David pulls out the numbers in boxes A and B and reports that their product is $$14$$. Justin then claims that the product of the numbers in boxes B and C is $$16$$, and Richard states the product of the numbers in boxes C and D to be $$18$$. Finally, Palmer announces the product of the numbers in boxes D and A. If $$k$$ is the number that Palmer says, what is $$20k$$?

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