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

- \\frac{PQ}{QR}\\) > 2
- \\frac{PQ}{QR}\\) = 2
- \\frac{PQ}{QR}\\) < 2
- can’t be determined

\\frac{PQ}{QR}\\) < 2

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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 = x^{2}

=> x^{2} - 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 "**

Choice C is the correct answer.

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