During an international climate summit, a group of delegates is seated in a single straigh… — State PSC Exam

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

A
$49$
$54$ Cevap
C
$55$
D
$38$

Cevap

The correct answer is

54

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

33^{\text{rd}}

from the left (Julian's new position) and

22^{\text{nd}}

from the right (Nadia's original position). Therefore, the total number of delegates is

33 + 22 - 1 = 54

Adım Adım Çözüm

Determine the position of a single specific seat from both ends of the row.

Nadia's original seat is given as

22^{\text{nd}}

from the right end. After the interchange, Julian moves into this seat, and his new position is given as

33^{\text{rd}}

from the left end. Thus, this single seat is

33^{\text{rd}}

from the left and

22^{\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.

Apply the total count formula:

\text{Total} = (\text{Position from Left}) + (\text{Position from Right}) - 1

\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.

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