Six lectures A, B, C, D, E and F, each of one hour duration, scheduled between 8:00 am and 2:00 pm Consider the following question and two statements: Question: Which lecture is in the third period? Statement- 1: Lecture F is preceded by A followed by C. Statement- 2: No lecture after lecture B. Which of the following is correct regarding the question and the statements?

The question asks which lecture is in the third period. There are 6 lectures (A, B, C, D, E, F) and 6 periods from 8:00 am to 2:00 pm. Analyze Statement 1: "Lecture F is preceded by A followed by C." This means the sequence A, C, F must occur in consecutive periods. Possible arrangements for A, C, F: 1. A in P1, C in P2, F in P3. (P3 is F) 2. A in P2, C in P3, F in P4. (P3 is C) 3. A in P3, C in P4, F in P5. (P3 is A) 4. A in P4, C in P5, F in P6. (P3 is one of D, E, B) Since there are multiple possibilities for the lecture in the third period (F, C, A, or others), Statement 1 alone is not sufficient. Analyze Statement 2: "No lecture after lecture B." This implies that B is the last lecture, i.e., B is in P6. P1 _ P2 _ P3 _ P4 _ P5 _ P6 B This statement tells us nothing about the lecture in the third period (P3). Therefore, Statement 2 alone is not sufficient. Analyze Combined Statements 1 and 2: From Statement 2, B is in P6. From Statement 1, we have the sequence A, C, F. Let's combine these: Case 1: A in P1, C in P2, F in P3. P1: A P2: C P3: F P4: (D/E) P5: (D/E) P6: B In this case, the lecture in P3 is F. Case 2: A in P2, C in P3, F in P4. P1: (D/E) P2: A P3: C P4: F P5: (D/E) P6: B In this case, the lecture in P3 is C. Case 3: A in P3, C in P4, F in P5. P1: (D/E) P2: (D/E) P3: A P4: C P5: F P6: B In this case, the lecture in P3 is A. We cannot have A, C, F starting from P4 because F would then be in P6, which is already occupied by B. Since there are still multiple possibilities for the lecture in the third period (F, C, or A) even after combining both statements, both statements together are not sufficient to answer the question. Therefore, option D is correct. The final answer is $\boxed{D}$