ITPEC FE Morning October 2023 Question 51
The ten members of a project team hold meetings with each other with the conditions below. If two (2) members are to be added to the team, how many additional meetings will be held compared to if there were ten members?
[Conditions]
- •Meetings are held one-on-one.
- •Each member holds one meeting with every other member.
Explanation
21 more meetings — count unordered pairs before and after the two members join.
Each pair of members meets once, so the number of meetings is the number of pairs, n(n − 1) ÷ 2.
- •10 members: 10 × 9 ÷ 2 = 45
- •12 members: 12 × 11 ÷ 2 = 66
- •Additional meetings: 66 − 45 = 21
Check directly: each newcomer meets the 10 original members, 2 × 10 = 20, plus one meeting between the two newcomers, 21.
Answer (b)
Why not others:
- •(a) 12 — the new team size, not a count of meetings; the newcomers alone need 20 meetings with the original members
- •(c) 22 — 2 × 11: each newcomer's 11 meetings are added up, so the meeting between the two newcomers is counted twice
- •(d) 42 — 12 × 11 − 10 × 9: ordered pairs, counting every meeting once from each side
Key rule: One-to-one links among n people number n(n − 1) ÷ 2; count each pair once, not once per participant.
Project Management · AI-written, may contain errors
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