Six lectures A, B, C, D, E and F , each of one hour duration, are scheduled between 8:00 a.m. 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 correct option is: Both Statement-1 and Statement-2 are not sufficient to answer the Question.

To understand why both statements together are insufficient, let us analyze the information provided step-by-step.

There are six lectures (A, B, C, D, E, and F) scheduled in six one-hour periods between 8:00 a.m. and 2:00 p.m.
The periods can be numbered as follows:
1st Period: 8:00 a.m. - 9:00 a.m.
2nd Period: 9:00 a.m. - 10:00 a.m.
3rd Period: 10:00 a.m. - 11:00 a.m.
4th Period: 11:00 a.m. - 12:00 p.m.
5th Period: 12:00 p.m. - 1:00 p.m.
6th Period: 1:00 p.m. - 2:00 p.m.

Our goal is to uniquely determine which lecture takes place during the third period.

Step 1: Analyzing Statement-1
Statement-1 states: "Lecture F is preceded by A and followed by C."
This tells us the relative order of A, F, and C, which must be A followed by F followed by C (represented as the block: A - F - C).
However, Statement-1 does not give any absolute positioning or time slots for this block. The block could be scheduled in periods 1-2-3, 2-3-4, 3-4-5, or 4-5-6. Therefore, Statement-1 alone is not sufficient.

Step 2: Analyzing Statement-2
Statement-2 states: "There is no lecture after lecture B."
Since there are six periods in total, this directly places lecture B in the 6th period (1:00 p.m. - 2:00 p.m.).
Knowing only that B is in the 6th period tells us nothing about which lecture is scheduled in the 3rd period. Therefore, Statement-2 alone is not sufficient.

Step 3: Combining Statement-1 and Statement-2
Let us combine the information from both statements:
- The 6th period is occupied by B.
- The block A - F - C must be placed in the remaining slots (periods 1 to 5).
- Two lectures, D and E, are still unplaced.

Let us try to arrange the lectures to see if the 3rd period is uniquely determined.
Case 1: Place the block A - F - C in periods 1, 2, and 3.
- Period 1: A
- Period 2: F
- Period 3: C
- Period 4: D (or E)
- Period 5: E (or D)
- Period 6: B
In this arrangement, the lecture in the third period is C.

Case 2: Place the block A - F - C in periods 2, 3, and 4.
- Period 1: D (or E)
- Period 2: A
- Period 3: F
- Period 4: C
- Period 5: E (or D)
- Period 6: B
In this arrangement, the lecture in the third period is F.

Conclusion:
Even when using both statements together, the lecture in the third period can be either C or F (or even A, D, or E depending on other valid arrangements). Since we cannot determine a unique lecture for the third period, both Statement-1 and Statement-2 together are not sufficient to answer the Question.