ITPEC FE Subject A October 2025 Question 41

Topic: Project Management

Eight (8) activities and milestones of a project are shown in the arrow diagram below. Which of the following is the critical path of this project?

A15D10E15B10C15F15G5H10Legend:Activity nameNumber of daysrequiredDummy

Explanation

A → C → E → H, 55 days — the critical path is the longest route from start to finish, and the dummy makes E wait for C.

The dummy takes 0 days but runs from the milestone after B and C to the start of E, so E cannot start until C is done. Every route from start to finish:

RouteDaysTotal
A → C → dummy → E → H15 + 15 + 0 + 15 + 1055
A → D → E → H15 + 10 + 15 + 1050
A → C → F → G15 + 15 + 15 + 550
B → dummy → E → H10 + 0 + 15 + 1035
B → F → G10 + 15 + 530

The same result by earliest times: the lower-left milestone is reached at day 30 (A then C beats B's 10), E starts at day 30 (the dummy beats D's day 25), and the finish is day 30 + 15 + 10 = 55.

Answer (a)

Why not others:

  • •(b) A, C, F, G — 50 days: after C, the lower branch F → G takes 20 days, less than dummy → E → H at 25
  • •(c) B, E, H — 35 days: starting with B reaches the lower-left milestone at day 10 instead of day 30 via A and C
  • •(d) B, F, G — 30 days, the shortest route of all

Key rule: At each milestone take the latest of the incoming arrows (a dummy counts 0 days); the arrows that set those maxima form the critical path.

Project Management · AI-written, may contain errors

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