Study the following information carefully and answer the given questions:
Seven persons A, B, C, D, E, F, and G are sitting around a circular table, but not necessarily in the same order.
Some of them face towards the centre, and some face away from the centre.
F sits third to the right of A. The immediate neighbours of A face the same direction but opposite as A. A faces the same direction as B but not towards the centre. One person sits between A and C. D sits 2nd to the left of C. E sits 2nd to the left of G and face in the same direction. F and D face opposite direction as E.
How many persons sit between B and F (counting clockwise from F)?
Correct Answer :
Four
Solution :
The correct option is Four.
Let's analyze the given information step-by-step to determine the seating arrangement of seven persons (A, B, C, D, E, F, and G) around a circular table.
Step 1: Understanding the statements and directions
1. A faces the same direction as B but not towards the centre. This means both A and B face away from the centre (Outside).
2. F sits third to the right of A. Since A faces away from the centre (Outside), counting 3 places to the right of A places F in that position.
3. The immediate neighbours of A face the same direction, which is opposite to A. Since A faces away from the centre, both immediate neighbours of A must face towards the centre (Inside).
4. One person sits between A and C. There are two possibilities for C's position relative to A.
5. D sits 2nd to the left of C.
6. E sits 2nd to the left of G and both E and G face in the same direction.
7. F and D face opposite direction as E.
Step 2: Placing the persons around the circular table (7 positions, numbered 1 to 7 clockwise)
Let position 1 be A (Facing: Outside).
Since A faces outside, right of A is counter-clockwise (7, 6, 5...) and left of A is clockwise (2, 3, 4...).
F sits 3rd to the right of A → F is at position 5.
Immediate neighbours of A are at positions 2 and 7. Both face Inside.
Now consider the placement of C (1 person between A and C):
C can be at position 3 or position 6.
If C is at position 6 (which is a neighbour of A, facing Inside):
D sits 2nd to the left of C. Since C faces Inside, left of C (at position 6) is clockwise, which leads to position 4 for D.
Remaining positions for E and G are 2, 3, and 7.
If G is at 7 (facing Inside): 2nd to the left of G (Inside) is clockwise → position 2 for E. Both E and G face Inside.
Then B must be at position 3.
Let's verify all facing directions:
- A faces Outside
- B (at position 3) faces Outside
- Immediate neighbours of A (positions 2 and 7) face Inside → E (at 2) and G (at 7) face Inside.
- E and G face the same direction → Both face Inside.
- F and D face opposite direction to E → Since E faces Inside, F and D must face Outside.
- C (at position 6) faces Inside (neighbour of A).
Let's summarize the final seating order clockwise (from 1 to 7):
1. A (Outside)
2. E (Inside)
3. B (Outside)
4. D (Outside)
5. F (Outside)
6. C (Inside)
7. G (Inside)
Step 3: Answer the question
We need to find the number of persons sitting between B and F when counting clockwise from F:
Starting at F (position 5) and moving clockwise: 5 (F) → 6 (C) → 7 (G) → 1 (A) → 2 (E) → 3 (B).
The persons sitting between F and B counting clockwise are C, G, A, and E.
Therefore, there are exactly 4 (Four) persons sitting between B and F when counting clockwise from F.
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