A, B, C, D, E, F and G are sitting around a circular table facing the centre. B sits second to the right of C. E sits third to the left of B. D is the immediate neighbour of G and A. F sits second to the left of G. How many people sit between A and B when counted from the left of A?
Correct Answer :
Two
Solution :
The correct option is Two.
Let's solve the circular seating arrangement step-by-step:
Step 1: Total positions and direction
There are 7 people: A, B, C, D, E, F, and G sitting around a circular table facing the centre.
Facing the centre means:
- Right = Counter-clockwise direction
- Left = Clockwise direction
Step 2: Position C and B
"B sits second to the right of C."
Let's place C at position 1 (say, bottom of the circle).
Moving 2 places counter-clockwise (right of C), B is placed at position 3.
Step 3: Position E
"E sits third to the left of B."
From B (position 3), move 3 places clockwise (left of B):
Position 3 → 2 → 1 → 7.
So, E is placed at position 7.
Step 4: Position F and G
"F sits second to the left of G."
The available positions so far are 2, 4, 5, 6.
If G is at position 6, then second to the left of G (clockwise) is position 4. So F is at position 4.
(If G were at 5, second to its left would be 3, which is occupied by B. If G were at 4, second to its left would be 2, which would leave no room for D to be between G and A).
Step 5: Position D and A
"D is the immediate neighbour of G and A."
Since G is at position 6 and E is at position 7, the only available spot adjacent to G is position 5.
Thus, D is at position 5, and A is at position 4.
Wait, let's re-verify F and G with A and D:
If G is at position 6, D is at position 5, and A is at position 4.
Then "F sits second to the left of G" means F must be at position 4, but A is at position 4.
Let's re-arrange:
Let's number positions 1 to 7 clockwise:
1. B sits second to the right of C:
If C is at position 1, facing centre:
Right of C (counter-clockwise) means position 7, 6, etc.
Let's define standard Clockwise = Left, Counter-Clockwise = Right.
Position 1 = C
Position 7 = 1st right of C
Position 6 = 2nd right of C = B
So B is at 6.
2. E sits third to the left of B:
Left of B (clockwise) starting from 6:
1st left = 7
2nd left = 1 (C)
3rd left = 2
So E is at position 2.
3. F sits second to the left of G:
Left of G is clockwise.
If G is at position 4, 2nd left of G is position 6 (B - occupied).
If G is at position 3, 2nd left of G is position 5.
If G is at position 7, 2nd left of G is position 2 (E - occupied).
Let's try G at position 3:
F is at 2nd left of G (clockwise) = position 5.
Remaining positions for D and A are 4 and 7.
Since "D is the immediate neighbour of G and A", and G is at 3, D must be adjacent to G, so D is at 4.
Then A is at 7 (adjacent to D at 4? Wait, in a circle of 7, position 4 is adjacent to 3 and 5. Position 7 is adjacent to 6 and 1).
So D at 4 is between G (3) and... wait, D needs to be between G and A. If G is 3 and D is 4, then A must be at 5, but F is at 5! That doesn't work.
Let's re-evaluate all positions counter-clockwise (1 to 7):
Let positions be 1, 2, 3, 4, 5, 6, 7 in counter-clockwise order.
Facing centre:
Right = Counter-clockwise (increasing numbers)
Left = Clockwise (decreasing numbers)
- C is at 1.
- B is 2nd right of C ⇒ B is at 3.
- E is 3rd left of B ⇒ E is at 3 - 3 = 7 (or 0 ≡ 7).
- Now remaining positions: 2, 4, 5, 6.
- "D is the immediate neighbour of G and A" ⇒ D must sit between G and A (G-D-A or A-D-G).
- "F sits second to the left of G" ⇒ F is 2 positions clockwise (minus 2) from G.
Let's test position of G:
Case A: G is at 5.
- D must be at 6 or 4.
- If D is at 6, then A is at 7 (occupied by E) - Invalid.
- If D is at 4, then A is at 2.
- F sits 2nd left of G (5 - 2 = 3, occupied by B) - Invalid.
Case B: G is at 4.
- D must be at 5, then A is at 6.
- F sits 2nd left of G (4 - 2 = 2).
Let's check positions:
Position 1 = C
Position 2 = F
Position 3 = B
Position 4 = G
Position 5 = D
Position 6 = A
Position 7 = E
Let's verify all conditions for this arrangement (1 to 7 Counter-Clockwise):
1. B sits 2nd to the right of C: C(1) → 1st right is F(2) → 2nd right is B(3). (Correct)
2. E sits 3rd to the left of B: B(3) → 1st left is F(2) → 2nd left is C(1) → 3rd left is E(7). (Correct)
3. D is immediate neighbour of G and A: D(5) is between G(4) and A(6). (Correct)
4. F sits 2nd to the left of G: G(4) → 1st left is B(3) → 2nd left is F(2). (Correct)
Step 6: Answer the question
Question: "How many people sit between A and B when counted from the left of A?"
A is at position 6.
Left of A means going clockwise (decreasing order: 5, 4, 3...):
From A(6), going to the left (clockwise):
- 1st to the left of A is D(5)
- 2nd to the left of A is G(4)
- 3rd to the left of A is B(3)
The people sitting between A and B when counted from the left of A are D and G.
Therefore, there are 2 people (D and G) between A and B.
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