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? Six persons P, Q, R, S, T and U are sitting around a circular table facing the center not necessarily in the same order. Consider the following statements:
• P sits next to S and T.
• Q sits diametrically opposite to P.
• The shortest distance between S and R is equal to the shortest distance between T and U.
Based on the above statements, Q is a neighbor of- Four persons P, Q, R and S are to be seated in a row, all facing the same direction, but not necessarily in the same order. P and R cannot sit adjacent to each other. S should be seated to the right of Q. The number of distinct seating arrangements possible is:
- 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:
