P, Q, R, S, and T have launched a new startup. Two of them are siblings. The office of the startup has just three rooms. All of them agree that the siblings should not share the same room.
If S and Q are single children, and the room allocations shown below are acceptable to all,PR TS Q
PQ RT S
then, which one of the given options is the siblings?
| PR | TS | Q |
|---|
| PQ | RT | S |
|---|
- AP and T
- BP and S
- CT and Q
- DT and R
Solution & Step-by-step Explanation
Startup Room Allocation Puzzle: Identifying Siblings
This problem requires identifying the sibling pair among five individuals (P, Q, R, S, T) based on specific room allocation rules within a startup.
Key Constraints and Deductions
- Individuals involved: P, Q, R, S, T.
- Number of rooms: 3.
- Number of siblings: Exactly 2.
- Rule 1: Siblings must occupy different rooms.
- Condition 1: S is a single child, hence cannot be one of the siblings.
- Condition 2: Q is a single child, hence cannot be one of the siblings.
Based on these conditions, the siblings must be selected from the remaining individuals: P, R, and T.
The possible sibling pairs are therefore:
- P and R
- P and T
- R and T
Evaluating Provided Options
The options given for the sibling pair are:
- 1. P and T
- 2. P and S
- 3. T and Q
- 4. T and R
Applying the deductions from the constraints:
- Option 2 (P and S) is eliminated because S cannot be a sibling.
- Option 3 (T and Q) is eliminated because Q cannot be a sibling.
This leaves Option 1 (P and T) and Option 4 (T and R) as the only potential correct answers, as both pairs consist of individuals from the set {P, R, T}.
Final Determination of Siblings
The problem implies a unique solution exists. We must select the pair for which a valid room allocation is possible, adhering to all rules. If P and T are the siblings, they must be in separate rooms.
Consider the allocation: Room 1 contains {P, R}, Room 2 contains {T, S}, and Room 3 contains {Q}.
- This allocation uses 3 rooms for the 5 people.
- P and T are in different rooms (Room 1 and Room 2, respectively), satisfying the sibling rule.
- S and Q are placed, and their status as single children does not prevent this allocation.
Since a valid allocation exists where P and T are siblings and adhere to all rules, this pair is the correct answer.
This problem requires identifying the sibling pair among five individuals (P, Q, R, S, T) based on specific room allocation rules within a startup.
Key Constraints and Deductions
- Individuals involved: P, Q, R, S, T.
- Number of rooms: 3.
- Number of siblings: Exactly 2.
- Rule 1: Siblings must occupy different rooms.
- Condition 1: S is a single child, hence cannot be one of the siblings.
- Condition 2: Q is a single child, hence cannot be one of the siblings.
Based on these conditions, the siblings must be selected from the remaining individuals: P, R, and T.
The possible sibling pairs are therefore:
- P and R
- P and T
- R and T
Evaluating Provided Options
The options given for the sibling pair are:
- 1. P and T
- 2. P and S
- 3. T and Q
- 4. T and R
Applying the deductions from the constraints:
- Option 2 (P and S) is eliminated because S cannot be a sibling.
- Option 3 (T and Q) is eliminated because Q cannot be a sibling.
This leaves Option 1 (P and T) and Option 4 (T and R) as the only potential correct answers, as both pairs consist of individuals from the set {P, R, T}.
Final Determination of Siblings
The problem implies a unique solution exists. We must select the pair for which a valid room allocation is possible, adhering to all rules. If P and T are the siblings, they must be in separate rooms.
Consider the allocation: Room 1 contains {P, R}, Room 2 contains {T, S}, and Room 3 contains {Q}.
- This allocation uses 3 rooms for the 5 people.
- P and T are in different rooms (Room 1 and Room 2, respectively), satisfying the sibling rule.
- S and Q are placed, and their status as single children does not prevent this allocation.
Since a valid allocation exists where P and T are siblings and adhere to all rules, this pair is the correct answer.