A number can be considered “purple” if it is halfway between two perfect squares. Is \(x\) purple?

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A number can be considered “purple” if it is halfway between two perfect squares. Is \(x\) purple?

(1) The product of \(x\) and \(2\) is equal to the sum of two squares.

(2) The average of \(x\) and the square of \(2\) is \(7.\)

Answer: D

Source: Veritas Prep