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 ?

Correct Answer: (B) 2

Given points $P, Q, R$ lie on a straight line with $PQ : QR = 3 : 5$. Depending on the relative ordering of the points along the line, two distinct geometric configurations are possible: (1) If $Q$ lies between $P$ and $R$, then $PR = PQ + QR = 3 + 5 = 8$, yielding $PQ : PR = 3 : 8$. (2) If $P$ lies between $Q$ and $R$, then $PR = QR - PQ = 5 - 3 = 2$, yielding $PQ : PR = 3 : 2$. ($R$ cannot lie between $P$ and $Q$ because $QR = 5 > PQ = 3$). Thus, there are exactly $n = 2$ possible values for the ratio.