Correct Option (4)
The question requires identifying the lecture scheduled in the third period. There are six lectures (A, B, C, D, E, F) each of one-hour duration, scheduled consecutively from 8:00 AM to 2:00 PM, implying six distinct time slots or periods.
Statement 1: "Lecture F is preceded by A and followed by C." This establishes a fixed, consecutive sequence of lectures A-F-C. Given six periods, this block can be placed in multiple ways:
- If A-F-C occupies periods 1-3: A is in the 1st period, F in the 2nd, and C in the 3rd.
- If A-F-C occupies periods 2-4: A is in the 2nd period, F in the 3rd, and C in the 4th.
- If A-F-C occupies periods 3-5: A is in the 3rd period, F in the 4th, and C in the 5th.
Since the lecture in the third period could be C, F, or A, Statement 1 alone is insufficient to provide a unique answer.
Statement 2: "There is no lecture after lecture B." This directly implies that lecture B is scheduled in the sixth and final period (1:00 PM to 2:00 PM). This statement provides no information regarding the lectures in periods 1 through 5, including the third period. Therefore, Statement 2 alone is insufficient.
Combining Statement 1 and Statement 2:
From Statement 2, we know B is in the 6th period. The A-F-C block must still occupy three consecutive periods within the remaining five slots (periods 1-5). The possible placements for A-F-C remain:
- A-F-C in periods 1-3: The third period is C.
- A-F-C in periods 2-4: The third period is F.
- A-F-C in periods 3-5: The third period is A.
Even with both statements combined, the lecture in the third period (C, F, or A) cannot be uniquely determined. Consequently, both Statement 1 and Statement 2 are not sufficient to answer the question.
Incorrect Options:
Option 1 is incorrect because Statement 1 alone allows for three different lectures (A, F, or C) to be in the third period, thus not providing a unique answer.
Option 2 is incorrect because Statement 2 alone only fixes the position of lecture B in the sixth period and offers no information about the lecture in the third period.
Option 3 is incorrect because, as demonstrated, combining both Statement 1 and Statement 2 still does not lead to a unique identification of the lecture in the third period. Therefore, both statements together are not sufficient.