Eight students A, B, C, D, E, F, G and H sit around a circular table, equidistant from each other, facing the centre of the table, not necessarily in the same order. B and D sit neither adjacent to C nor opposite to C. A sits in between E and D, and F sits in between B and H. Which one of the following is definitely correct?
- (a) B sits in between A and G
- (b) C sits opposite to G
- (c) E sits opposite to F
- (d) None of the above ✓ UPSC's answer
Why the answer is (d)
• Fix A's seat. A sits between E and D, and F sits between B and H. B and D must be neither next to C nor opposite C.
• Checking every seating that meets these conditions gives exactly six arrangements. Going round the table from A they are: A D G B F H C E; A D G C H F B E; A D H F B G C E; A E B F H C G D; A E C G B F H D; A E C H F B G D.
• (a) B is never between A and G — B's neighbours are always F with G or E.
• (b) C is opposite G in only two of the six arrangements (in others C is opposite E or H).
• (c) E is opposite F in only two of the six arrangements (in others E is opposite B or C).
• So none of (a), (b), (c) is definitely correct, option (d).
Why the other options are wrong
- (a) B sits in between A and G
- In every valid arrangement B's neighbours are F and either G or E; B is never between A and G.
- (b) C sits opposite to G
- C is opposite G in only two of the six valid arrangements, so it is not definitely true.
- (c) E sits opposite to F
- E is opposite F in only two of the six valid arrangements, so it is not definitely true.
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.