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Difficulty: MediumOrder and Ranking

During an international climate summit, a group of delegates is seated in a single straight row facing the main stage. Julian is seated 17th17^{\text{th}} from the left end of the row, while Nadia is seated 22nd22^{\text{nd}} from the right end. If Julian and Nadia interchange their seats, Julian's new position becomes 33rd33^{\text{rd}} from the left end. Based on this information, what is the total number of delegates seated in the row?

  1. A
    4949
  2. 5454Answer
  3. C
    5555
  4. D
    3838

Answer

The correct answer is 5454.
The total number of individuals in a line can be determined by adding a single position's rank from the left and its rank from the right, then subtracting 1 to account for double-counting. After interchanging seats, Julian moves to Nadia's original seat. This seat is 33rd33^{\text{rd}} from the left (Julian's new position) and 22nd22^{\text{nd}} from the right (Nadia's original position). Therefore, the total number of delegates is 33+22−1=5433 + 22 - 1 = 54.

Step-by-Step Solution

1
Determine the position of a single specific seat from both ends of the row.
Nadia's original seat is given as 22nd22^{\text{nd}} from the right end. After the interchange, Julian moves into this seat, and his new position is given as 33rd33^{\text{rd}} from the left end. Thus, this single seat is 33rd33^{\text{rd}} from the left and 22nd22^{\text{nd}} from the right.
To calculate the total number of people in a row, we must know the exact position of one distinct point measured from both the left and right extremes.
2
Apply the total count formula: Total=(Position from Left)+(Position from Right)−1\text{Total} = (\text{Position from Left}) + (\text{Position from Right}) - 1.
Total=33+22−1=54\text{Total} = 33 + 22 - 1 = 54.
Adding the left and right positions counts the specific intersection seat twice. We must subtract 1 to ensure a correct, un-duplicated headcount.

Key Concept

Order and Ranking
Estimated Time:1m 0s
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Topics

Order and Ranking

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