CAT Quantitative Aptitude Questions | Geometry Questions for CAT - Triangles

The question is from CAT Geometry - Quadrilateral. Its a very basic question testing the basic properties of the quadrilaterals. CAT Geometry questions are heavily tested in CAT exam. Make sure you master Geometry problems.

Question 36: If PQ || RS, find the value of x

1. 7
2. 3
3. Both A & B
4. None of these

Explanatory Answer

Method of solving this CAT Question from Quadrilaterals: It is a very basic question.

If PQ || RS => ∆POQ ~ ∆ROS
=> \\frac{1}{(x+5)}\\) = \\frac{x-2}{13x-31}\\)
=> 13x - 31 = (x-2)(x+5)
=> 13x – 31 = x² – 2x + 5x – 10
=> 13x – 31 = x² + 3x – 10
=> x² – 10x +21 = 0
=> x² – 7x – 3x +21 = 0
=> x(x-7) -3(x-7) = 0
=> (x-3)(x-7) = 0
=> x = 3, 7

The question is "If PQ || RS, find the value of x "

Hence, the answer is Both A & B

Choice C is the correct answer.