Five friends P, Q, R, S and T went camping. At night, they sleep in a row. P, Q and T need not sleep next to each other. P, Q and T need to avoid Q since he snored loudly. P and S wanted to avoid Q as he usually hugged people in sleep. Assuming everyone is in the sleeping arrangements, which of the following must be true? A. RSPTQ B. SRPQT C. QRSPT D. QTPSR

GATE 2020 · General Aptitude · Round Table Arrangement · medium

Answer: C. QRSPT

  1. Identify who cannot be adjacent to Q: Q snores and hugs, so: P must not be next to Q (snoring), T must not be next to Q (snoring), P must not be next to Q (hugging), S must not be next to Q (hugging). Combining: Q cannot be adjacent to P, S, or T. The only person who can be next to Q is R.
  2. Check option A: RSPTQ: Positions: R=1, S=2, P=3, T=4, Q=5. Q at position 5 is adjacent only to T at position 4. T is in Q's forbidden adjacency list. INVALID.
  3. Check option B: SRPQT: Positions: S=1, R=2, P=3, Q=4, T=5. Q at position 4 is adjacent to P(3) and T(5). Both are forbidden. INVALID.
  4. Check option C: QRSPT: Positions: Q=1, R=2, S=3, P=4, T=5. Q at position 1 is adjacent only to R(2). R is allowed to be next to Q. Also: S(3) is not adjacent to Q(1) - distance 2. P(4) is not adjacent to Q(1) - distance 3. T(5) is not adjacent to Q(1) - distance 4. All constraints satisfied. VALID.
  5. Check option D: QTPSR: Positions: Q=1, T=2, P=3, S=4, R=5. Q at position 1 is adjacent to T(2). T is forbidden. INVALID.