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Q40·CSAT · Prelims 2022

Circular seating arrangement with specific positional rules

ReasoningSeating ArrangementFactual single● Hard

Question

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?

Options

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

Answer

Explanation

Map the seating arrangements using 8 numbered slots. The structural groups are block 1: `E-A-D` and block 2: `H-F-B` (or `B-F-H`).

Let's test one valid configuration to verify if any option is a universal truth: Place `E` at 1, `A` at 2, `D` at 3. We must place the block `H-F-B` and the remaining elements `C` and `G`. Constraint: `C` cannot be adjacent or opposite to `D` (3) or `B`. Opposite of 3 is 7. Adjacent to 3 are 2 and 4. Thus, `C` cannot be at 7 or 4. Let's place the `H-F-B` block at 4, 5, 6 \implies B=6. Opposite to `B`(6) is 2. Adjacent are 5, 7. So `C` cannot be at 6, 2, 5, or 7. This leaves slot 8 for `C`. The remaining slot 7 goes to `G`.

Check constraints for this layout: `E`(1), `A`(2), `D`(3), `H`(4), `F`(5), `B`(6), `G`(7), `C`(8).

Is `C`(8) opposite `D`(3) or `B`(6)? Opposites are 4 and 2. No.
Is `C`(8) adjacent to `D`(3) or `B`(6)? Adjacents are 2, 4 and 5, 7. No.

This is a perfectly valid layout.

Evaluate the options against this layout:

(a) `B` sits between `A` and `G`: `B`(6) is between `F`(5) and `G`(7). (False)
(b) `C` sits opposite `G`: `C`(8) is opposite `H`(4). (False)
(c) `E` sits opposite `F`: `E`(1) is opposite `F`(5). (True in this layout).

Now, test if (c) is definitely true by building an alternative valid layout. Place `E` at 8, `A` at 1, `D` at 2. Place `G` at 3, `C` at 4, `H` at 5, `F` at 6, `B` at 7. Check constraints: `C`(4) is opposite `E`(8). Not opposite `B`(7) or `D`(2). `C`(4) is adjacent to `G`(3) and `H`(5). Not adjacent to `B`(7) or `D`(2). This is also a perfectly valid layout.

Evaluate (c) against this layout:

(c) `E` sits opposite `F`: `E`(8) is opposite `C`(4), not `F`(6). (False)

Since no option holds true across all mathematically valid configurations, none are definitely correct.

In circular seating puzzles, if you can build two completely valid table configurations that yield different outcomes for the given options, the answer is always "None of the above."

Answer: (d).

Question details

Year

2022

Paper

CSAT

Question

Q40

Section

Logical & Analytical Reasoning

Sub-topic

Seating Arrangement

Type

Factual single

Difficulty

Hard

Source hint

Eight students A, B, C, D, E, F, G, H in a circle

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