Eight friends A, B, C, D, E, F, H and G are sitting around a circular table facing each other for a group discussion. A is opposite F and second to the right of E. G is between C and A. H is to the left of E. Who is sitting to the immediate left of A?
- AEither G or D
- BB
- CC
- DEither B or D
Solution & Step-by-step Explanation
Let us trace the positions of the eight friends around the circular table (facing inwards):
A is opposite F and second to the right of E: Let E be at position 1 (say, bottom). Since everyone is facing inward, the second to the right of E is position 3. So, A is at position 3. Since F is opposite A, F is placed at position 7.
H is to the left of E: Since E is at position 1, his immediate left is position 2. So, H is at position 2.
G is between C and A: A is at position 3. The neighbor at position 2 is already occupied by H. Therefore, G must be at position 4, and C must be at position 5.
Remaining friends: The remaining positions are 6 and 8. The remaining persons are B and D. Thus, B and D will occupy positions 6 and 8 in any order.
Let us map the circle sequentially clockwise or counter-clockwise:
If we look at A (at position 3), his immediate right is position 4 (occupied by G).
His immediate left is position 2 (occupied by H) or position 8 if we trace the other side. Let's arrange more formally:
Let E be at 6 o'clock.
Second to the right of E (counter-clockwise) is 9 o'clock. So, A = 9 o'clock.
F is opposite A, so F = 3 o'clock.
H is to the immediate left of E (clockwise), so H = 5 o'clock.
G is between C and A. Since 5 o'clock is taken by H, G must be at 10:30 or 12 o'clock. More precisely, positions from E (6 o'clock) going counter-clockwise:
E is at Pos 1.
Right of E: Pos 2, Pos 3 (A), Pos 4.
A is second to the right of E → if E is at 1, right is 2, then 3. So A = 3.
F is opposite A → F = 7.
H is to the left of E → H = 8.
G is between C and A → since A is 3, and 2 is empty but G needs to be between C and A, if G is 2, then C must be 1 (which is E, not possible). Hence, G must be at 4 and C must be at 5.
This leaves positions 6 and 8 vacant for B and D.
Now, looking at A (at position 3): its immediate right is position 4 (G) and its immediate left is position 2.
Wait, let's re-verify the remaining open spots. The positions are 1 (E), 2 (Vacant), 3 (A), 4 (G), 5 (C), 7 (F), 8 (H).
The vacant positions for B and D are 2 and 6.
The immediate left of A (at position 3) is position 2.
Therefore, the person sitting to the immediate left of A must be either B or D.
A is opposite F and second to the right of E: Let E be at position 1 (say, bottom). Since everyone is facing inward, the second to the right of E is position 3. So, A is at position 3. Since F is opposite A, F is placed at position 7.
H is to the left of E: Since E is at position 1, his immediate left is position 2. So, H is at position 2.
G is between C and A: A is at position 3. The neighbor at position 2 is already occupied by H. Therefore, G must be at position 4, and C must be at position 5.
Remaining friends: The remaining positions are 6 and 8. The remaining persons are B and D. Thus, B and D will occupy positions 6 and 8 in any order.
Let us map the circle sequentially clockwise or counter-clockwise:
If we look at A (at position 3), his immediate right is position 4 (occupied by G).
His immediate left is position 2 (occupied by H) or position 8 if we trace the other side. Let's arrange more formally:
Let E be at 6 o'clock.
Second to the right of E (counter-clockwise) is 9 o'clock. So, A = 9 o'clock.
F is opposite A, so F = 3 o'clock.
H is to the immediate left of E (clockwise), so H = 5 o'clock.
G is between C and A. Since 5 o'clock is taken by H, G must be at 10:30 or 12 o'clock. More precisely, positions from E (6 o'clock) going counter-clockwise:
E is at Pos 1.
Right of E: Pos 2, Pos 3 (A), Pos 4.
A is second to the right of E → if E is at 1, right is 2, then 3. So A = 3.
F is opposite A → F = 7.
H is to the left of E → H = 8.
G is between C and A → since A is 3, and 2 is empty but G needs to be between C and A, if G is 2, then C must be 1 (which is E, not possible). Hence, G must be at 4 and C must be at 5.
This leaves positions 6 and 8 vacant for B and D.
Now, looking at A (at position 3): its immediate right is position 4 (G) and its immediate left is position 2.
Wait, let's re-verify the remaining open spots. The positions are 1 (E), 2 (Vacant), 3 (A), 4 (G), 5 (C), 7 (F), 8 (H).
The vacant positions for B and D are 2 and 6.
The immediate left of A (at position 3) is position 2.
Therefore, the person sitting to the immediate left of A must be either B or D.