Question

There are three points P, Q and R on a straight line such that PQ : QR = 3 : 5. If n is the number of possible values of PQ : PR, then what is n equal to ? 
1. 1
2. 2
3. 3
4. 4

Answer 1

Correct Answer - Option 2 : 2

Given:

PQ : QR = 3 : 5

Calculation:

CASE - 1 

Assuming PQ = 3x, QR = 5x and PR = PQ + QR, we get

PQ : PR = 3x : (3x + 5x)

⇒ PQ : PR = 3 : 8

CASE - 2

Assuming PQ = 3x, QR = 5x and PR = QR - PQ, we get

PQ : PR = 3x : (5x - 3x)

⇒ PQ : PR = 3 : 2

So, we have n = 2 possible values.

Hence, option 2 is correct.

 The order of points is not fixed. So, we have to check for all other possible cases.