CAT Quant Practice Problems

Question: Consider a square ABCD with midpoints E, F, G, H of AB, BC, CD and DA respectively. Let L denote the line passing through F and H. Consider points P and Q, on L and inside ABCD, such that the angles APD and BQC both equal 120°. What is the ratio of the area of ABQCDP to the remaining area inside ABCD?

\(\frac{{4\sqrt 2 }}{3}\)
\(2 + \sqrt 3 \)
\(\frac{{10 - 3\sqrt 2 }}{9}\)
\(1 + \frac{1}{{\sqrt 3 }}\)
\(2\sqrt 3 - 1\)
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