The following is a network diagram for a project.

According to the PMBOK® Guide, the Critical Path is the sequence of activities that represents the longest path through a project, which determines the shortest possible project duration.

Critical Path Method (CPM): To identify the critical path, the duration of all activities on each possible path from start to finish must be summed. The path with the highest total duration is the critical path.

Analysis of the Paths (Based on standard PMI Network Diagram Question 279):

Path A-B-D-G: $5 + 5 + 8 + 3 = 21$ days.

Path A-B-E-G: $5 + 5 + 4 + 3 = 17$ days.

Path A-C-E-G: $5 + 9 + 4 + 3 = 21$ days.

Path A-C-F-G: $5 + 9 + 10 + 3 = 27$ days.

Determination: Since Path A-C-F-G has the longest duration (27 days), it is the critical path. Any delay in activities A, C, F, or G will result in a direct delay to the project completion date. Activities on this path have zero float.

Comparison with other options:

A, B, and D: These paths have shorter total durations (21, 17, and 21 days respectively). Therefore, these paths have Total Float, meaning the activities on these paths can be delayed to some extent without affecting the overall project finish date. Only the longest path is considered " Critical " in standard CPM.