GATE EC 2019 Set 1 — Question 6

Let the four positions in the line be P1, P2, P3, P4 from left to right. The people are Rahul (R), Mathew (M), Seema (S), and Lohit (L). The professions are Engineer (E), Doctor (D), Teacher (T), and Dancer (Da).Let's analyze the clues:Let's combine clues:
From Clue 2, we have two main cases for the ends:
Case 1: Lohit is at P1, and the Engineer is at P4.
Line: L ENow, consider the (Doctor) Seema (D S) block from Clue 5. The Doctor is a person, and Seema is a person. So, the D S block refers to the positions of the Doctor and Seema.
Possible positions for (D S) block:

• If (D S) is (P1, P2): This would mean Lohit is the Doctor, and Seema is at P2. So, L(D) S _ E. The remaining people are R and M. The remaining professions are T and Da. So, R and M must be T and Da. The line is L(D) S R M(E) (R and M fill the remaining spots).

Let's check this arrangement: L(D) S R M(E)

• Clue 1: M is not next to S. (M is at P4, S is at P2. They are not adjacent. Consistent.)
• Clue 2: Two people between L and E. (L is at P1, M is E at P4. S and R are between them. Consistent.)
• Clue 3: R is not D. (R is at P3, L is D. Consistent.)
• Clue 4: T and Da are next to each other. (S and R are T and Da, and they are adjacent. Consistent.)
• Clue 5: (Doctor) Seema. (L is the Doctor at P1, S is at P2. L is to the left of S. Consistent.)

This arrangement is consistent with all clues.
In this arrangement, Mathew (M) is the Engineer.Let's quickly check other possibilities for completeness, though we found a consistent solution.

• If (D S) is (P2, P3): L D S E. This means the person at P2 is the Doctor, and Seema is at P3. So, L (Doctor) S E. The remaining people are R and M. The remaining professions are T and Da. So, R and M are T and Da. The line is L R(D) S M(E) or L M(D) S R(E).
• If L R(D) S M(E): R is the Doctor. This contradicts Clue 3 (Rahul is not a doctor). So, this is not possible.
• If L M(D) S R(E): M is the Doctor. S is at P3. M is at P2. This violates Clue 1 (Mathew is not next to Seema). So, this is not possible.
• If (D S) is (P3, P4): L _ D S. This means the person at P3 is the Doctor, and Seema is at P4. But P4 is the Engineer. So, Seema is the Engineer. The line is L M R(D) S(E) or L R M(D) S(E).
• If L M R(D) S(E): S is at P4. M is at P2. This violates Clue 1 (Mathew is not next to Seema). So, this is not possible.
• If L R M(D) S(E): S is at P4. R is at P2. M is at P3. This violates Clue 1 (Mathew is not next to Seema). So, this is not possible.

Case 2: Engineer is at P1, and Lohit is at P4.
Line: E L

• If (D S) is (P1, P2): This means the Engineer is the Doctor. This is impossible as they are distinct professions.
• If (D S) is (P2, P3): E D S L. This means the person at P2 is the Doctor, and Seema is at P3. The remaining people are R and M. The remaining professions are T and Da. So, R and M are T and Da. The line is M(E) R(D) S L or R(E) M(D) S L.
• If M(E) R(D) S L: R is the Doctor. This contradicts Clue 3 (Rahul is not a doctor). So, this is not possible.
• If R(E) M(D) S L: M is the Doctor. S is at P3. M is at P2. This violates Clue 1 (Mathew is not next to Seema). So, this is not possible.
• If (D S) is (P3, P4): E _ D S. This means the person at P3 is the Doctor, and Seema is at P4. But P4 is Lohit. So, Seema is Lohit. This is impossible as they are distinct people.

The only consistent arrangement is from Case 1, where Lohit is at P1 (Doctor), Seema is at P2 (Teacher/Dancer), Rahul is at P3 (Teacher/Dancer), and Mathew is at P4 (Engineer).Therefore, Mathew is the Engineer.The final answer is $\boxed{\text{Mathew}}$