Seven cars P, Q, R, S, T, U and V are parked in a row not necessarily in that order. The cars T and U should be parked next to each other. The cars S and V also should be parked next to each other, whereas P and Q cannot be parked next to each other. Q and S must be parked next to each other. R is parked to the immediate right of V. T is parked to the left of U.
Based on the above statements, the only INCORRECT option given below is:
Car Parking Rules
Seven cars (P, Q, R, S, T, U, V) are parked in a row. The following rules apply:
- T and U are adjacent, with T to the left of U (forming a TU block).
- S and V are adjacent.
- Q and S are adjacent.
- R is immediately to the right of V (forming a VR block).
- P and Q cannot be parked next to each other.
Parking Block Formation
Combining rules establishes fixed car blocks:
- "R is immediate right of V" and "S and V are next to each other" implies the block SVR.
- "Q and S must be next to each other" combined with SVR implies the block QSVR.
- The other fixed block is TU.
- The arrangement involves placing the blocks P, TU, and QSVR.
Row Arrangement Scenarios
We list possible arrangements of P, TU, and QSVR, ensuring P and Q are not adjacent. Since QSVR starts with Q, P cannot be immediately before it if TU is placed last, nor can TU be placed between P and QSVR if P is before it.
Valid arrangements are:
- P, TU, QSVR → PTUQSVR
- TU, QSVR, P → TUQSVERP
- QSVR, P, TU → QSVERPTU
- QSVR, TU, P → QSVERTUP
Option Statement Verification
We check each statement against the valid arrangements to find the one that is false.
Option A: There are two cars parked in between Q and V.
- In PTUQSVR: Q(pos 4), V(pos 6). Car S is between (1 car). False.
- In TUQSVERP: Q(pos 3), V(pos 5). Car S is between (1 car). False.
- In QSVERPTU: Q(pos 1), V(pos 3). Car S is between (1 car). False.
- In QSVERTUP: Q(pos 1), V(pos 3). Car S is between (1 car). False.
This statement is false in all valid scenarios.
Option B: Q and R are not parked together.
In all valid arrangements, Q and R are separated by at least one car. This statement is True.
Option C: V is the only car parked in between S and R.
The block SVR inherently means V is the only car between S and R. This statement is True.
Option D: Car P is parked at the extreme end.
- PTUQSVR: P is at the left end. True.
- TUQSVERP: P is at the right end. True.
- QSVERPTU: P is in the middle (pos 5). False.
- QSVERTUP: P is at the right end. True.
This statement is not always true.
Incorrect Parking Statement Result
The question asks for the *only INCORRECT* option. Option A is false in all valid arrangements, making it definitively incorrect. While Option D is not always true, Option A is always false, fitting the criteria for the incorrect statement.
Important Questions from Seating Arrangement
- P and Q have been allotted a hostel room with two beds, a study table, and an almirah. P is an avid bird-watcher and wants to sit at the table and watch birds outside the window. Q does not mind that as long as his bed is close to the ceiling fan.
Which one of the following arrangements suits them the most? - P, Q, R, S, T and U are seated around a circular table. R is seated two places to the right of Q. P is seated three places to the left of R. S is seated opposite U. If P and U now switch seats, which of the following must necessarily be true?
Five persons P, Q, R, S and T are sitting in a row not necessarily in the same order. Q and R are separated by one person, and S should not be seated adjacent to Q.
The number of distinct seating arrangements possible is:
- S, T, U, V, W, X, Y, and Z are seated around a circular table. T's neighbours are Y and V. Z is seated third to the left of T and second to the right of S. U's neighbours are S and Y; and T and W are not seated opposite each other. Who is third to the left of V?
- Five persons P, Q, R, S and T are to be seated in a row, all facing the same direction, but not necessarily in the same order. P and T cannot be seated at either end of the row. P should not be seated adjacent to S. R is to be seated at the second position from the left end of the row. The number of distinct seating arrangements possible is:
