Explanation

This question has a particular diagram about a survey, but you could think of it as a schematic for a type of counting, permutation, and/or probability exercise that crops up on GMAT questions. The key here is that certain junctures are independent of others. For example, there are two ways to take the first fork. Looking past that, there is a juncture that can be traversed by top, middle or bottom. Whether we take top, middle, or bottom at that juncture is completely unaffected by whether we took the top or bottom path at the first juncture. For that reason, there are three ways to take the middle juncture for each of the two ways of taking the first juncture. In this context, "for each" is a key phrase hinting at multiplication. For that reason, there are ways of getting past the second juncture (including getting past the first). There are four ways of crossing the final juncture, so the number of paths is .

The correct answer is (C).