The correct answer is: A. greater than or equal to latest event time of preceding node.
The latest start of an activity is the latest time that the activity can start without delaying the project. It is equal to or greater than the latest event time of the preceding node, which is the latest time that the preceding node can finish without delaying the project.
For example, consider the following project network diagram:
The latest start time of activity A is 10, because it can start as soon as activity B finishes, which has a latest finish time of 10. The latest start time of activity C is 15, because it can start as soon as activity A finishes, which has a latest start time of 10. The latest start time of activity D is 20, because it can start as soon as activity C finishes, which has a latest start time of 15.
The latest start time of an activity can never be less than the latest event time of the preceding node, because if it were, the activity would have to start before the preceding node finishes, which would delay the project.