ITPEC IP October 2019 Question 52
In a project team that is required to convey information on a one-to-one basis, when the members increase from six (6) people to ten (10) people, by how many times does the number of paths that is required for communicating information increase?
Explanation
3 times — the number of one-to-one paths is the number of pairs of members, which grows much faster than the team.
With n members, every pair needs one path: n(n − 1) ÷ 2.
- •6 members: 6 × 5 ÷ 2 = 15 paths
- •10 members: 10 × 9 ÷ 2 = 45 paths
- •Increase: 45 ÷ 15 = 3 times
Answer (c)
Why not others:
- •(a) 1.5 and (b) 2.5 — neither fits the counts: 15 × 1.5 = 22.5 and 15 × 2.5 = 37.5 paths are not even whole numbers; treating paths as proportional to the team, 10 ÷ 6 ≈ 1.7, also underestimates the growth
- •(d) 6 — halves only one of the counts: 10 × 9 = 90 against 15 gives 90 ÷ 15 = 6
Key rule: Communication paths grow with the square of the team size, n(n − 1) ÷ 2, which is why adding people raises communication overhead faster than capacity.
Project Management · AI-written, may contain errors
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