Question

P, Q, R and S are four towns. One can travel between P and Q along 3 direct paths, between Q and S along 4 direct paths, and between P and R along 4 direct paths. There is no direct path between P and S, while there are a few direct paths between Q and R and also between R and S. One can travel from P to S either via Q, or via R, or via Q followed by R, respectively, in exactly 62 possible ways. One can also travel from Q to R either directly, or via P, or via S, in exactly 27 possible ways. Then, the number of direct paths between Q and R is:

• A. 0
• B. 2
• C. 3
• D. 4
• E. 5

Hint:

In path counting problems, use multiplication for sequential paths and addition for alternative routes. Set up equations based on the given totals.

Answer 1

The Correct Option is C