Six lectures A B C D E and F, each of one hour duration, are scheduled between 8:00 am, and 2:00 p.m. Consider the Question and two Statements given below: Question: Which lecture is in the third period? Statement- 1: Lecture F is preceded by A and followed by C Statement- 2: There is no lecture after lecture B. Which one of the following is correct in respect of the Question and the Statements?

The question asks to identify the lecture in the third period (P3) out of six lectures (A, B, C, D, E, F) scheduled in six one-hour periods from 8:00 am to 2:00 p.m. Let's analyze each statement: Statement-1: Lecture F is preceded by A and followed by C. This implies a fixed sequence of three lectures: A - F - C. These three lectures can occupy different positions: 1. P1=A, P2=F, P3=C (Then P3 is C) 2. P2=A, P3=F, P4=C (Then P3 is F) 3. P3=A, P4=F, P5=C (Then P3 is A) 4. P4=A, P5=F, P6=C (Then P3 is one of the remaining lectures D, E, B) Since P3 can be C, F, A, or one of the others, Statement-1 alone is not sufficient to determine the lecture in the third period. Statement-2: There is no lecture after lecture B. This means lecture B is the last lecture. So, P6 = B. This statement only tells us about P6. It provides no information about P1, P2, P3, P4, or P5. Therefore, Statement-2 alone is not sufficient to determine the lecture in the third period. Now, let's combine both statements: Statement-1: A - F - C Statement-2: P6 = B We know P6 = B. Let's re-evaluate the possibilities for A - F - C: 1. If A - F - C are in P1, P2, P3: P1=A, P2=F, P3=C. This is consistent with P6=B. (P3 is C) 2. If A - F - C are in P2, P3, P4: P2=A, P3=F, P4=C. This is consistent with P6=B. (P3 is F) 3. If A - F - C are in P3, P4, P5: P3=A, P4=F, P5=C. This is consistent with P6=B. (P3 is A) 4. If A - F - C are in P4, P5, P6: P4=A, P5=F, P6=C. This contradicts Statement-2 (P6=B). So, this possibility is ruled out. Even with both statements combined, the lecture in the third period (P3) could be C, F, or A. We cannot uniquely determine which lecture is in the third period. Therefore, both Statement-1 and Statement-2 are not sufficient to answer the question. The final answer is D