A group of seven students—P, Q, R, S, T, U, V—are to be seated in a single row of seven chairs, numbered 1 to 7 from left to right. The seating arrangement must conform to the following conditions: Q must be seated immediately to the left of S. R cannot be seated in chair 1 or chair 7. P must be seated in an even-numbered chair. U must be seated to the right of T. If V is seated in chair 3, then P must be seated in chair 6. If U is seated in chair 5, and P is seated in chair 2, which of the following statements must be true?
- AV is seated in chair 3.
- BS is seated in chair 7.
- CR is seated in chair 6.
- DT is seated in chair 4.
Show answer & explanationAnswer & explanation
Correct answer: D. T is seated in chair 4.
If U is in chair 5 and P is in chair 2, then Q and S must be in chairs 6 and 7 respectively to satisfy the Q-S block and P being in an even chair. Since U is to the right of T, and U is in chair 5, T must be in a chair to the left of 5. As P is in chair 2, T cannot be in chair 2. If T were in chair 1, then R cannot be in chair 1 or 7, and R cannot be in chair 2, 5, 6, 7. This leaves chair 3 or 4 for R. If T is in chair 4, then R can be in chair 3. Considering the available chairs and rules, T must be in chair 4.
Why the other options are wrong
- A. V could be in chair 3, but it does not HAVE to be. It is a possibility, not a necessity. If V is in chair 3, P must be in chair 6, but P is given as in chair 2. So V cannot be in chair 3.
- B. S must be in chair 7 because Q is immediately to its left, and P is in chair 2 and U in chair 5, leaving chairs 6 and 7 for the QS block. This statement is true, but the question asks what MUST be true, and other options might also be true.
- C. R cannot be in chair 6 because Q and S occupy chairs 6 and 7 respectively if U is in chair 5 and P is in chair 2, and Q must be immediately to the left of S.
Deduction from Multiple Fixed Positions
When several elements are assigned fixed positions or relationships, deduce the necessary placement of other elements by systematically applying all remaining rules and constraints.
- Fixed positions drastically reduce possibilities.
- Chaining deductions is crucial.
- Identify conflicts with existing rules immediately.
Memory trick: Fixed spots on the map, link them up to find the hidden path.