In the table below the check marks indicate all languages spoken by five people: Paula, Quentin, Robert, Sally and Terence. For example, Paula speaks only Chinese and English.
These five people form three teams, Team 1, Team 2 and Team 3. Each team has either 2 or 3 members. A team is said to speak a particular language if at least one of its members speak that language.
The following facts are known:
1. Each team speaks exactly four languages and has the same number of members.
2. English and Chinese are spoken by all three teams, Basque and French by exactly two teams and the other languages by exactly one team.
3. None of the teams include both Quentin and Robert.
4. Paula and Sally are together in exactly two teams.
5. Robert is in Team 1 and Quentin is in Team 3.
Who among the five people is a member of all teams?
Correct Answer :
Paula
Solution :
Let's deduce the team members step by step:
1. English and Chinese are spoken by all three teams.
2. Basque and French are spoken by exactly two teams, whereas Arabic and Dutch are spoken by exactly one team.
3. Paula and Sally are together in exactly two teams. Since they must be together in two teams, let these be Team 1 and Team 3.
4. Robert is in Team 1 and Quentin is in Team 3 (and they are never in the same team).
This gives the following membership for Team 1 and Team 3:
- Team 1: Robert, Paula, Sally
- Team 3: Quentin, Paula, Sally
Since Team 2 must speak Dutch (which only Terence speaks), Terence is in Team 2. To satisfy the constraint that each team has the same number of members (or using the team size constraints), we determine that:
- Team 2: Terence and Paula
Reviewing the team list:
- Team 1: Robert, Paula, Sally
- Team 2: Terence, Paula
- Team 3: Quentin, Paula, Sally
We can clearly see that Paula is a member of all three teams (Team 1, Team 2, and Team 3).
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