CAT Quantitative Aptitude Questions | Geometry Questions for CAT - Triangles

The question is from the topic lines. In this problem, it tests our understanding on basic properties of a line. CAT Geometry questions are heavily tested in CAT exam. Make sure you master Geometry problems.

Question 40: In the below figure, If \\frac{PR}{PQ}\\) = \\frac{PQ}{QR}\\), then

1. \\frac{PQ}{QR}\\) > 2
2. \\frac{PQ}{QR}\\) = 2
3. \\frac{PQ}{QR}\\) < 2
4. can’t be determined

Explanatory Answer

Method of solving this CAT Question from Triangles: It is a very basic question. Let's start with the given details.

Given, \\frac{PR}{PQ}\\) = \\frac{PQ}{RQ}\\)
Here, PR = PQ + RQ
=> 1 + \\frac{RQ}{PQ}\\) = \\frac{PQ}{RQ}\\)
Let \\frac{PQ}{RQ}\\) = x
=> 1+ \\frac{1}{x}\\) = x
=> x+ 1 = x²
=> x² - x - 1 = 0
=> x = \\frac{(+1±√(1+4))}{2}\\) = \\frac{1±√5}{2}\\) , Since PQ – RQ > 0
=> x = \\frac{1+√5}{2}\\) which is between 1 and 2

The question is " If \\frac{PR}{PQ}\\) = \\frac{PQ}{RQ}\\), then "

Hence, the answer is \\frac{PQ}{QR}\\) < 2

Choice C is the correct answer.