2015 Mock AIME I Problem 1: Picking Numbers from a Hat
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 \(20k\)?