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Question

Difficulty: HardOrder and Ranking

At a busy immigration checkpoint, a single line of passengers is waiting to be processed. Fatima is standing 22nd22^{\text{nd}} from the front of the line, while Diego is 32nd32^{\text{nd}} from the back.

Due to a lane reassignment, Fatima and Diego completely swap their positions in the line. After the swap, Fatima becomes 40th40^{\text{th}} from the front.

A third passenger, Haruki, is standing exactly halfway between Diego's new position and Fatima's new position.

If 55 passengers at the very back of the line give up and leave, what is Haruki's new position counting from the back of the line?

  1. 35th35^{\text{th}}Answer
  2. B
    36th36^{\text{th}}
  3. C
    37th37^{\text{th}}
  4. D
    41st41^{\text{st}}

Answer

The correct answer is the 36th36^{\text{th}} position.
By determining the initial total number of passengers (40+32−1=7140 + 32 - 1 = 71) and identifying Haruki's position from the front (the midpoint of 2222 and 4040, which is 3131), we can find Haruki's final position from the back after 55 people leave. The new total is 6666, making Haruki's position from the back 66−31+1=3666 - 31 + 1 = 36.

Step-by-Step Solution

1
Calculate the initial total number of passengers in the line.
Total = 40+32−1=7140 + 32 - 1 = 71 passengers.
After the swap, Fatima moves to Diego's old position. Since her new rank is 40th40^{\text{th}} from the front and Diego's old rank was 32nd32^{\text{nd}} from the back, this single position's front and back ranks sum to the total plus one.
2
Determine Diego's new position from the front.
Diego is now 22nd22^{\text{nd}} from the front.
Because Fatima and Diego completely swapped places, Diego assumes Fatima's original position.
3
Find Haruki's position from the front of the line.
Haruki's position = 22+402=31st\frac{22 + 40}{2} = 31^{\text{st}} from the front.
Haruki is exactly halfway between Diego's new position (22nd22^{\text{nd}}) and Fatima's new position (40th40^{\text{th}}).
4
Calculate the new total number of passengers and Haruki's position from the back.
New total = 71−5=6671 - 5 = 66. Haruki's back rank = 66−31+1=3666 - 31 + 1 = 36.
Since 55 people left from the very back, Haruki's front rank (31st31^{\text{st}}) remains unchanged, but the overall line length shrinks to 6666. The standard formula for finding a back rank is (Total - Front Rank + 1).

Key Concept

Position Interchange and Midpoint Ranking
Estimated Time:2m 30s
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Topics

Order and Ranking

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