Points \(M\) and \(P\) lie on square \(LNQR,\) and \(LM = PQ.\) What is the length of the line segment \(PQ?\)

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Points \(M\) and \(P\) lie on square \(LNQR,\) and \(LM = PQ.\) What is the length of the line segment \(PQ?\)

(1) \(PR=\dfrac{4\sqrt{10}}3\)
(2) The ratio of the area of the unshaded region to the total area of the shaded region is 2 to 1.

[spoiler]OA=D[/spoiler]

Source: GMAT Prep
Source: — Data Sufficiency |