Question

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: \[ \begin{array}{|c|c|c|} P, R & T, S & Q
P, Q & R, T & S
\end{array} \] Then, which one of the given options is the siblings?

• A. P and T
• B. P and S
• C. T and Q
• D. T and R

Hint:

For arrangement-based problems, focus on identifying pairs that consistently avoid violating the given constraints. Use elimination to rule out pairs that fail to satisfy the conditions in any scenario.

Answer 1

The Correct Option is A

Step 1: Understand the constraints of the problem.
- Siblings are not allowed to share the same room in any allocation.
- S and Q are individual children without siblings, eliminating them from sibling consideration. Step 2: Evaluate the provided room allocations:
- In the first allocation: \([P, R], [T, S], [Q]\) \(P\) and \(R\) share a room, \(T\) and \(S\) share a room, and \(Q\) is alone.
- In the second allocation: \([P, Q], [R, T], [S]\) \(P\) and \(Q\) share a room, \(R\) and \(T\) share a room, and \(S\) is alone. Step 3: Identify the sibling pair based on the given conditions:
- From the rooming patterns, \(P\) and \(T\) never share a room in either arrangement.
- Other pairs, such as \(P\) and \(R\), \(T\) and \(R\), or \(P\) and \(Q\), do share a room in at least one allocation, disqualifying them as siblings.
Therefore, the sibling pair is P and T, as their allocations align with the condition that siblings never share a room. Final Answer: \[ \boxed{{(1) P and T}} \]