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?
  1. \(\frac{{4\sqrt 2 }}{3}\)
  2. \(2 + \sqrt 3 \)
  3. \(\frac{{10 - 3\sqrt 2 }}{9}\)
  4. \(1 + \frac{1}{{\sqrt 3 }}\)
  5. \(2\sqrt 3 - 1\)

Correct Option:5

Consider side of square as 10 units. So HD=5 and HP=$\frac{5}{\sqrt3}$ . So now area of triangle HPD=$\frac{12.5}{\sqrt3}$. Also Area APD=Area BQC=2×AreaHPD=$\frac{25}{\sqrt3}$. So numerator of required answer is $100-\frac{50}{\sqrt3}$ and denominator as $\frac{50}{\sqrt3}$. Solving we get answer as $2\sqrt{3}-1$.

CAT 2019 Online Course

CAT Quant Questions with Video Solutions

CAT Quant Practice Problems
4.6 (92%) 15 votes