Eight friends, , , , , , , and are seated in a circle facing the centre. is between and . is third to the left of . is between and . is third to the right of . Which of the following must be true?
(A) is seated next to .
(B) is seated next to .
(C) is seated next to .
(D) is seated third to the right of .
Eight friends, , , , , , , and are seated in a circle facing the centre. is between and . is third to the left of . is between and . is third to the right of . Which of the following must be true?
(A) is seated next to .
(B) is seated next to .
(C) is seated next to .
(D) is seated third to the right of .
Solution
We have 8 friends seated in a circle facing the center. Let's use the clues to find their positions.
Let's place at position 1 (we can start anywhere in a circle).
Since is third to the left of , count counterclockwise:
So is at position 6.
Positions so far: ,
Since is between and , and is at position 1, must be adjacent to .
Place at position 8 (to the left of ), then must be at position 7 (so is between and ).
Positions: , , ,
Remaining people are , , , for positions 2, 3, 4, 5.
Since is third to the right of (clockwise), let's try at position 2.
Count clockwise:
So is at position 5.
Positions: , , , , ,
Since is between and , and is at position 5, must be adjacent to .
Positions 3 and 4 are available. Place at position 4.
For to be between and , place at position 3.
Final positions: , , , , , , ,
Circular arrangement (clockwise):
Now check each option:
(A) is seated next to : is at position 7, is at position 6. They are adjacent. True.
(B) is seated next to : is at position 5, is at position 2. Not adjacent. False.
(C) is seated next to : is at position 1, is at position 2. They are adjacent. True.
(D) is seated third to the right of : is at position 4. Third to the right: gives position 7, which is , not . False.
Both (A) and (C) must be true.
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