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)
• There are 6 time slots (8-9, 9-10, 10-11, 11-12, 12-1, 1-2) for lectures A, B, C, D, E, F.
• Statement-1 states F is preceded by A and followed by C, creating the fixed sequence A-F-C in three consecutive slots.
• This sequence can occupy slots 1-2-3, 2-3-4, 3-4-5, or 4-5-6, leaving multiple possibilities for the third slot (F, C, or others depending on position).
• Statement-2 states no lecture is after B, meaning B is in the last slot (slot 6).
• Combining both, if B is in slot 6, the A-F-C block can be in slots 1-2-3 (3rd is F), 2-3-4 (3rd is F), or 3-4-5 (3rd is A). Since the third lecture could be F or A, the question cannot be answered uniquely.
Why the other options are wrong
- (a) Statement-1 alone is sufficient to answer the Question
- Statement-1 alone allows the A-F-C block to be in positions 1-3, 2-4, 3-5, or 4-6, resulting in different lectures (F, C, or others) occupying the third slot.
- (b) Statement-2 alone is sufficient to answer the Question
- Statement-2 alone only fixes B in the last slot, leaving the positions of A, C, D, E, and F completely undetermined for the third slot.
- (c) Both Statement-1 and Statement-2 are sufficient to answer the Question
- Even with both statements, the A-F-C block can be placed in slots 1-3, 2-4, or 3-5 (since B is in slot 6), leading to different answers (F or A) for the third slot.
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.