Solution
Understanding the set :-
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This is a teams set, in this set with the help of given constraints you need to find the members of each team.
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In this set we have the five people - Paula, Quentin, Robert, Sally and Terence, speaking two languages each, as shown in the table.
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Also, we are given that each team has equal members, which is whether 2 or 3.
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And, each team speaks exactly 4 languages.
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Also, in this set there is no constraint as teams being mutually exclusive, which implies a person can be a member of one or more team simultaneously.
| Arabic | Basque | Chinese | Dutch | English | French | |
|---|---|---|---|---|---|---|
| Paula | ✓ | ✓ | ||||
| Quentin | ✓ | ✓ | ||||
| Robert | ✓ | ✓ | ||||
| Sally | ✓ | ✓ | ||||
| Terence | ✓ | ✓ |
| Languages Spoken | Arabic, french, | Dutch, english | |
|---|---|---|---|
| Teams | Team 1 | Team 2 | Team 3 |
| Member | R | Q | |
| Member | |||
| Member |
Clue 5 says,
Robert is in Team 1 and Quentin is in Team 3.
We can directly add this to the table.
Also, we can fill the language spoken by them in the first row.
R - Arabic, French
Q - Dutch, English
| Arabic | Basque | Chinese | Dutch | English | French | |
|---|---|---|---|---|---|---|
| Paula | ✓ | ✓ | ||||
| Quentin | ✓ | ✓ | ||||
| Robert | ✓ | ✓ | ||||
| Sally | ✓ | ✓ | ||||
| Terence | ✓ |
| Languages Spoken | Arabic, french | English, Basque, chinese | Dutch, english, Chinese, Basque |
|---|---|---|---|
| Teams | Team 1 | Team 2 | Team 3 |
| Member | R | P | Q |
| Member | S | P | |
| Member | S |
Now, clue 4 says,
Paula and Sally are together in exactly two teams.
We know, P speaks - Chinese and English
while, S speaks - Basque and English
Now, if P and S is in team 1, then total language will become 5 , which will contradict clue 1.
Therefore, P and S will be in team 2 and team 3.
Therefore, each team will have 3 members each.
| Arabic | Basque | Chinese | Dutch | English | French | |
|---|---|---|---|---|---|---|
| Paula | ✓ | ✓ | ||||
| Quentin | ✓ | ✓ | ||||
| Robert | ✓ | ✓ | ||||
| Sally | ✓ | ✓ | ||||
| Terence | ✓ | ✓ |
| Languages Spoken | Arabic, french | English, Basque, chinese, French | Dutch, english, Chinese, Basque |
|---|---|---|---|
| Teams | Team 1 | Team 2 | Team 3 |
| Member | R | P | Q |
| Member | S | P | |
| Member | T | S |
Now, we only want one member (P & S are already there) and one more language for team 2.
Therefore, last member will be one among Q, R, T.
- For Q -
Q is already in team 3 with P and S => including Q with P & S will make both the teams same,
Therefore, Q can't be in team 2.
- For R :-
languages spoken - Arabic and french
if R is in team 2, it's total languages will become 5
Therefore, R also can't be in team 2.
Therefore, T will be in team 2,
And, 4 languages spoken by team 2 will be - English, Basque, chinese, and french.
| Arabic | Basque | Chinese | Dutch | English | French | |
|---|---|---|---|---|---|---|
| Paula | ✓ | ✓ | ||||
| Quentin | ✓ | ✓ | ||||
| Robert | ✓ | ✓ | ||||
| Sally | ✓ | ✓ | ||||
| Terence | ✓ | ✓ |
| Languages Spoken | Arabic, french, Chinese | English, Basque, chinese, French | Dutch, english, Chinese, Basque |
|---|---|---|---|
| Teams | Team 1 | Team 2 | Team 3 |
| Member | R | P | Q |
| Member | T | S | P |
| Member | T | S |
For team 1,
R is already a member.
Q can't be with R (clue 3)
=> we need two of P, S or T.
Now, clue 4 says, Paula and Sally are together in exactly two teams.
which , we found to be team 2 and team 3.
=> Other two members of team 1 will be T and, one of P or S.
| Arabic | Basque | Chinese | Dutch | English | French | |
|---|---|---|---|---|---|---|
| Paula | ✓ | ✓ | ||||
| Quentin | ✓ | ✓ | ||||
| Robert | ✓ | ✓ | ||||
| Sally | ✓ | ✓ | ||||
| Terence | ✓ | ✓ |
| Languages Spoken | Arabic, French, Chinese, English | English, Basque, Chinese, French | Dutch, English, Chinese, Basque |
|---|---|---|---|
| Teams | Team 1 | Team 2 | Team 3 |
| Member | R | P | Q |
| Member | T | S | P |
| Member | P | T | S |
Case - 1 : s in team 1 -
Languages spoken - Basque and English
But, it will make total languages in team 1 as 5.
Therefore, case is rejected.
Therefore, P will be in Team 1
And, 4 languages of team 1 will be - Arabic, French, Chinese and English.
| Arabic | Basque | Chinese | Dutch | English | French | |
|---|---|---|---|---|---|---|
| Paula | ✓ | ✓ | ||||
| Quentin | ✓ | ✓ | ||||
| Robert | ✓ | ✓ | ||||
| Sally | ✓ | ✓ | ||||
| Terence | ✓ | ✓ |
| Languages Spoken | Arabic, French, Chinese, English | English, Basque, Chinese, French | Dutch, English, Chinese, Basque |
|---|---|---|---|
| Teams | Team 1 | Team 2 | Team 3 |
| Member | R | P | Q |
| Member | T | S | P |
| Member | P | T | S |
AS Shown above among the given four people Sally is a part of exactly two teams.