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Zorluk: OrtaOrder and Ranking

In a straight row of cadets facing North for a morning assembly, Cadet Marcus is standing 15th15^{\text{th}} from the left end and Cadet Victor is standing 28th28^{\text{th}} from the right end. If they interchange their positions, Cadet Marcus becomes 35th35^{\text{th}} from the left end. What is Cadet Victor's new position from the right end?

  1. A
    47th47^{\text{th}}
  2. 48th48^{\text{th}}Cevap
  3. C
    49th49^{\text{th}}
  4. D
    62nd62^{\text{nd}}

Cevap

48th48^{\text{th}}
The correct answer accurately calculates the total number of cadets as 6262 and correctly applies the formula to find the rank from the opposite end (62−15+1=4862 - 15 + 1 = 48).

Adım Adım Çözüm

1
Calculate the total number of cadets in the row.
Total = 6262 cadets.
After the interchange, Marcus occupies Victor's original position. This physical spot is 35th35^{\text{th}} from the left and 28th28^{\text{th}} from the right. The total number of cadets is L+R−1=35+28−1=62L + R - 1 = 35 + 28 - 1 = 62.
2
Determine Victor's new position from the left.
Victor is now 15th15^{\text{th}} from the left.
During the interchange, Victor takes Marcus's original spot, which was given as 15th15^{\text{th}} from the left.
3
Calculate Victor's new position from the right end.
Victor is 48th48^{\text{th}} from the right.
Using the position conversion formula (Total - Position from left + 1), Victor's position from the right is 62−15+1=4862 - 15 + 1 = 48.

Anahtar Kavram

Position Interchange and Total Calculation in Linear Arrangements

Alternatif Yöntem

Since Marcus's position shifted by 2020 places (35−15=2035 - 15 = 20) during the interchange, Victor's position must also shift by the exact same number of places relative to his starting end. Therefore, Victor's new position from the right end is simply 28+20=48th28 + 20 = 48^{\text{th}}.
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Order and Ranking

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