Directions (70-74): Study the following information carefully and answer the questions given below:
Eight persons A, B, C, D, E, F, G and H sit around a square table in such a way that four persons sit on each of the four corner of the table and other four persons sit on the middle of side. The one who sits at the corner of table faces inside and the one who sits at the middle side of table faces outwards the centre of table. Persons sitting on opposite sides are exactly opposite to each other.
B sits immediate left of A. Three persons sit between B and C. One person sits between H and C. F sits just left of H but not face outside. E sits 2nd to the left of G. D sits near G.
Which of the following statement is true?
I. G faces Inside
II. C sits near E
III. D sits immediate left of G
Correct Answer :
All I, II and III
Solution :
To determine which of the statements are true, let us step-by-step construct the seating arrangement around the square table based on the given conditions.
Step 1: Understand the Seating Directions
There are 8 positions around the square table: 4 at the corners and 4 at the middle of the sides.
- The 4 corner positions face inside (towards the center). For these positions, "left" corresponds to the clockwise direction, and "right" corresponds to the counter-clockwise direction.
- The 4 middle-of-the-side positions face outside (away from the center). For these positions, "left" corresponds to the counter-clockwise direction, and "right" corresponds to the clockwise direction.
Step 2: Place F and H
We are given: "F sits just left of H but does not face outside."
Since F does not face outside, F must face inside and therefore sits at a corner.
For F to be just left of H while F is at a corner, H must face outside (sit at the middle of a side). If H is at a middle position (facing outside), its immediate left is in the counter-clockwise direction. Therefore, F must be at the corner immediately counter-clockwise to H.
Let us assign the positions as follows:
- H sits at a middle position (let's call it position 2).
- F sits at the corner to its left (position 1, facing inside).
Step 3: Place C and B
- "One person sits between H and C."
Since H is at position 2, C can sit either at position 4 or position 8. Let us analyze both cases:
Case A: C sits at position 4.
- "Three persons sit between B and C." This means B and C are opposite to each other. Since C is at position 4, B must be at position 8.
- "B sits immediate left of A." Since B is at position 8 (a middle position), A must sit at position 7 (corner, facing inside) so that B is to the immediate left (clockwise) of A. This gives: F = 1, H = 2, C = 4, A = 7, B = 8.
- Now we need to place D, E, and G in the remaining positions: 3, 5, and 6.
- "E sits 2nd to the left of G" and "D sits near G." If G is at position 3 (corner, facing inside), its left is clockwise, so 2nd to the left is position 5 (where E would sit). For D to sit near G, D must sit at position 2 or 4, but both are already occupied by H and C. Thus, Case A is invalid.
Case B: C sits at position 8.
- B sits opposite to C, so B is at position 4.
- Since B sits immediate left of A, and B (position 4) is adjacent to corner position 3, A must be at position 3 (corner, facing inside, so its left is clockwise at position 4).
This gives the occupied positions so far:
- Position 1 (Corner): F
- Position 2 (Middle): H
- Position 3 (Corner): A
- Position 4 (Middle): B
- Position 8 (Middle): C
Step 4: Place the Remaining Persons (D, E, G)
The remaining unoccupied positions are 5 (Corner), 6 (Middle), and 7 (Corner).
- "E sits 2nd to the left of G."
If G sits at position 5 (Corner, facing inside), the direction to its left is clockwise (towards 6 and 7). The position 2nd to the left of G is position 7. Thus, E must sit at position 7.
- "D sits near G."
Since G is at position 5, D must sit at the adjacent unoccupied position, which is position 6 (Middle). This placement is valid and satisfies all conditions.
Final Seating Arrangement (Clockwise):
1. F (Corner, facing Inside)
2. H (Middle, facing Outside)
3. A (Corner, facing Inside)
4. B (Middle, facing Outside)
5. G (Corner, facing Inside)
6. D (Middle, facing Outside)
7. E (Corner, facing Inside)
8. C (Middle, facing Outside)
Step 5: Verify the Statements
- I. G faces Inside: G sits at a corner (position 5), so G faces inside. (True)
- II. C sits near E: C is at position 8 and E is at position 7. They sit next to each other. (True)
- III. D sits immediate left of G: G is at position 5 (facing inside, so left is clockwise). Position 6 is immediate left of G, which is occupied by D. (True)
Therefore, all statements I, II, and III are true.
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