A project has activities A(5 days), B(3 days), C(7 days), and D(4 days). Activities A and B can start immediately. Activity C depends on A, and D depends on B. What is the critical path duration?
Correct Answer
C) 12 days
Path A-C takes 5+7=12 days, while path B-D takes 3+4=7 days. The critical path is A-C with 12 days total duration.
Why This Is the Correct Answer
The critical path is the longest sequence of dependent activities that determines the minimum project duration. In this network, there are two possible paths: A-C (5+7=12 days) and B-D (3+4=7 days). Since A-C takes 12 days and is longer than B-D's 7 days, the critical path duration is 12 days. Any delay in activities A or C will delay the entire project.
Why the Other Options Are Wrong
Option A: 7 days
7 days represents only the duration of path B-D, which is the shorter of the two paths and therefore not the critical path that determines project completion time.
Option B: 19 days
15 days incorrectly adds all activity durations (5+3+7+4=19) or makes an error in path calculation, but activities B and D run parallel to A and C, not in series.
Option D: 15 days
19 days incorrectly assumes all activities run in sequence (5+3+7+4=19), but the network shows A-B are parallel starting activities, not sequential.
Memory Technique
Remember 'LONGEST = CRITICAL' - the critical path is always the longest duration path through the network, as it controls when the project can finish
Reference Hint
Project Management/CPM sections in construction management references, typically found in chapters covering scheduling and critical path method
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