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 R and S also should be parked next to each other, whereas Q and S cannot be parked next to each other. R must be parked next to T. Q is parked to the immediate right of V. P is parked to the immediate right of Q. Which of the following is the correct order of parking from left to right?
A. SRTUVQP
B. TRSUVPQ
C. UTRSVPQ
D. TRSVUPQ
GATE 2021 · General Aptitude · Seating Arrangement · medium
Answer: The correct parking order left to right is S, R, T, U, V, Q, P (Answer A)
Build the mandatory adjacency chain: T next to U; R next to T; R next to S. The chain is U-T-R-S or its reverse S-R-T-U. This is a contiguous block of 4 cars.
Build the V-Q-P sequence: Q is immediately right of V, and P is immediately right of Q. This gives the fixed 3-car sequence V-Q-P in left-to-right order.
Join the two groups and check Q-S: Attach V-Q-P to the right end of S-R-T-U: full arrangement S-R-T-U-V-Q-P. Q is at position 6, S is at position 1 -- they are 5 apart and not adjacent. Constraint satisfied.
Verify all constraints for S-R-T-U-V-Q-P: R-S adjacent (positions 1-2): YES. R-T adjacent (positions 2-3): YES. T-U adjacent (positions 3-4): YES. V-Q adjacent (positions 5-6): YES. Q-P adjacent (positions 6-7): YES. Q-S not adjacent (positions 6 and 1): YES. All constraints satisfied.