Eight persons of different heights are stood in a queue. Only one person is ahead of the eighth tallest person. Number of persons ahead of the second tallest is same as the number of persons behind the second shortest person. The fifth tallest person stood immediately ahead of the second tallest. The eighth tallest person is immediately behind the tallest person. The third tallest person is exactly in between the fourth and the sixth tallest persons.
What is the position of the 'fourth tallest person'?
Show answer & explanation
Correct answer: D
Explanation
Let the 8 positions in the queue from front to back be numbered 1 to 8, and the heights in descending order be 1st to 8th.
• Position 2: The 8th tallest person is at position 2 (as only one person is ahead).
• Position 1: The 1st (tallest) person is at position 1 (immediately ahead of the 8th tallest).
• The 5th tallest is immediately ahead of the 2nd tallest: pos(5th) = pos(2nd) - 1.
• The number of persons ahead of the 2nd tallest equals the number of persons behind the 2nd shortest (7th tallest):
pos(2nd) + pos(7th) = 9
Since positions 1 and 2 are occupied, the valid placement is:
• Position 3: 5th tallest
• Position 4: 2nd tallest
• Position 5: 7th tallest
The remaining positions are 6, 7, and 8 for the 3rd, 4th, and 6th tallest persons.
• Since the 3rd tallest is exactly in between the 4th and 6th tallest persons, the 3rd tallest must be at position 7.
• However, the 4th and 6th tallest persons can occupy positions 6 and 8 in either order (4th at pos 6 and 6th at pos 8, OR 4th at pos 8 and 6th at pos 6).
Hence, the exact position of the 4th tallest person Cannot be determined.