Reasoning : Logical Reasoning & Analytical Ability

Q 87 / 325

UPSC CSE Prelims 2022

Six lectures A, B, C, D, E and F each of one hour duration, are scheduled between 8:00 AM to 2:00 PM.

Consider the question and two statements given below:

Question: Which lecture is in the third period?

  1. Statement 2: Lecture F is preceded by A and followed by C.
  2. Statement 3: There is no lecture after lecture B.

Which one of the following is correct in respect of the question and the statements?

EXPLANATION

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.