Four people are standing in a line facing you. They are Rahul, Mathew, Seema and Lohit. One is an engineer, one is a doctor, one a teacher and another a dancer. You are told that: 1. Mathew is not standing next to Seema 2. There are two people standing between Lohit and the engineer 3. Rahul is not a doctor 4. The teacher and the dancer are standing next to each other 5. Seema is turning to her right to speak to the doctor standing next to her Who among them is an engineer? A. Seema B. Lohit C. Rahul D. Mathew

GATE 2019 · General Aptitude · Seating Arrangement · medium

Answer: Mathew is the engineer.

  1. Apply Clue 2 to fix Lohit and engineer positions: Lohit and the engineer occupy positions 1 and 4. Lohit is not the engineer (they are different people), so one of {Rahul, Mathew, Seema} is in the position opposite to Lohit.
  2. Apply Clue 5 to locate Seema and the doctor: If Lohit is at position 1, Seema cannot be at position 4 (doctor would be off the line). Try Seema at position 1: then Lohit would also need position 1 - conflict. Try Seema at positions 2 or 3. If Seema is at position 2, doctor is at position 3. If Seema is at position 3, doctor is at position 4.
  3. Try Lohit at position 1 and test valid arrangements: Clue 1: Mathew not next to Seema. If Seema=2, Mathew cannot be at 3. So Mathew=4, Rahul=3. Doctor is at position 3 (Seema at 2, doctor to her right). Person at 3 is Rahul - but Clue 3 says Rahul is NOT a doctor. Contradiction. Try Seema=3, Mathew cannot be at 2 or 4. But only positions 2 and 4 are left for Mathew - contradiction.
  4. Try Lohit at position 4 and test valid arrangements: Engineer is at position 1. Clue 5: Seema turns right to doctor, so Seema is not at position 4 (no one to right). If Seema=1, doctor at 2. Clue 1: Mathew not next to Seema (pos 1), so Mathew not at 2. Mathew=3, Rahul=2. Doctor at position 2 = Rahul - contradicts Clue 3. Try Seema=2: doctor at 3. Clue 1: Mathew not at 1 or 3. Mathew cannot be 1 or 3, only position left is... positions 1 and 3 are for Rahul and Mathew. Mathew must avoid 1 (next to Seema at 2) and avoid 3 (next to Seema at 2). Contradiction. Try Seema=3: doctor at 4 = Lohit. Mathew not next to Seema (pos 3), so Mathew not at 2 or 4. Positions 1 and 2 left for Rahul and Mathew. Mathew not at 2, so Mathew=1, Rahul=2. Engineer at 1 = Mathew. Clue 4: teacher and dancer are adjacent. Remaining roles for Seema(3) and Rahul(2): teacher and dancer. Positions 2 and 3 are adjacent. Clue 4 satisfied.
  5. Confirm final arrangement: Check all clues: (1) Mathew(1) and Seema(3) are NOT adjacent - OK. (2) Two people (Rahul, Seema) between Lohit(4) and engineer Mathew(1) - OK. (3) Rahul is not the doctor (doctor is Lohit) - OK. (4) Rahul(2) and Seema(3) are adjacent (teacher and dancer) - OK. (5) Seema(3) turns right to position 4 = Lohit the doctor - OK.