A project has the following activities: A (5 days), B (3 days), C (7 days), D (4 days). Activities A and B can start immediately. Activity C depends on A completion. Activity D depends on both B and C completion. What is the critical path duration?
Correct Answer
C) 16 days
The critical path is A→C→D (5+7+4=16 days). The alternative path B→D (3+4=7 days) plus waiting for C completion still results in 16 days total project duration.
Why This Is the Correct Answer
The critical path is the longest sequence of dependent activities that determines the minimum project duration. Path A→C→D takes 5+7+4=16 days, which is longer than any other possible path. Since activity D cannot start until both B and C are complete, and C depends on A, the project cannot finish in less than 16 days regardless of when B completes.
Why the Other Options Are Wrong
Option A: 12 days
12 days would only account for activities A and C (5+7=12), but ignores that activity D still needs 4 additional days to complete after C finishes.
Option B: 14 days
14 days incorrectly assumes some overlap or parallel processing that isn't possible given the dependencies, or miscalculates the sequential durations of the critical path activities.
Option D: 19 days
19 days would incorrectly add all activity durations (5+3+7+4=19) without recognizing that activities A and B can run in parallel, not sequentially.
Memory Technique
Remember 'Longest Path Wins' - the critical path is always the longest sequence of activities, and you can't finish the project any faster than this path allows.
Reference Hint
Look up 'Critical Path Method (CPM)' or 'Project Scheduling' in construction management chapters, typically found in project management or scheduling sections.
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