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?

(a) Statement-1 alone is sufficient to answer the Question
(b) Statement-2 alone is sufficient to answer the Question
(c) Both Statement-1 and Statement-2 are sufficient to answer the Question
(d) Both Statement-1 and Statement-2 are not sufficient to answer the Question ✓ UPSC's answer

Why the answer is (d)

• The six one-hour slots between 8:00 a.m. and 2:00 p.m. are numbered 1 through 6, and the question asks which lecture occupies slot 3.

• Statement-1 says F is preceded by A and followed by C, fixing the consecutive block A-F-C, but that block can sit in slots (1,2,3), (2,3,4), (3,4,5), or (4,5,6), so slot 3 could be C, F, A, or one of the remaining lectures; Statement-1 alone is insufficient.

• Statement-2 says no lecture comes after B, which pins B to slot 6, but it gives no information about what occupies slot 3; Statement-2 alone is insufficient.

• Combining both statements, B occupies slot 6, so the A-F-C block cannot use slot 6, leaving only (1,2,3), (2,3,4), or (3,4,5) as possible placements.

• In those three placements slot 3 is respectively C, F, or A, and the remaining two lectures D and E fill the leftover slots in either order, so the identity of the lecture in slot 3 is still undetermined.

• Because neither statement alone nor both together uniquely identify the lecture in the third period, the correct choice is (d).

Why the other options are wrong

(a) Statement-1 alone is sufficient to answer the Question: Statement-1 allows the A-F-C block to occupy slots (1,2,3), (2,3,4), (3,4,5), or (4,5,6), producing four different candidates for slot 3, so it cannot by itself answer the question.
(b) Statement-2 alone is sufficient to answer the Question: Statement-2 only tells us that B is in the last slot (slot 6); it provides no constraint on which lecture is in slot 3, so it cannot by itself answer the question.
(c) Both Statement-1 and Statement-2 are sufficient to answer the Question: Even with B fixed in slot 6, the A-F-C block can still be placed in (1,2,3), (2,3,4), or (3,4,5), giving C, F, or A in slot 3 respectively, so the two statements together still do not yield a unique answer.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2022, held on 5 June 2022. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.