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In a fully automated logistics center, a single row of delivery robots is lined up facing the loading bay. Robot MM is positioned 27th27^{\text{th}} from the left end of the row, while Robot PP is positioned 31st31^{\text{st}} from the right end. If Robot MM and Robot PP interchange their positions, Robot PP becomes 48th48^{\text{th}} from the right end. Based on this rearrangement, what is the new position of Robot MM from the left end?

  1. A
    43rd43^{\text{rd}}
  2. 44th44^{\text{th}}Cevap
  3. C
    74th74^{\text{th}}
  4. D
    31st31^{\text{st}}

Cevap

The new position of Robot M from the left end is the 44th44^{\text{th}} position.
The correct answer accurately synthesizes the overlapping ranks. By analyzing Robot P's new position (which is Robot M's old position), we find the total number of robots is 27+48−1=7427 + 48 - 1 = 74. Robot M moves to Robot P's old position, which is 31st31^{\text{st}} from the right. Its position from the left is then calculated as 74−31+1=4474 - 31 + 1 = 44.

Adım Adım Çözüm

1
Identify the coordinates of the interchange spot.
Robot PP moves to Robot MM's original spot. This spot is known to be 27th27^{\text{th}} from the left end. After the swap, we are told Robot PP is now 48th48^{\text{th}} from the right end.
Establishing both the left and right ranks for a single spot allows us to calculate the total number of entities in the sequence.
2
Calculate the total number of delivery robots (NN).
N=(Rank from Left)+(Rank from Right)−1N = (\text{Rank from Left}) + (\text{Rank from Right}) - 1. Therefore, N=27+48−1=74N = 27 + 48 - 1 = 74 robots.
Adding the left and right ranks counts the robot sitting in that spot twice, so we must subtract 1 to get the accurate total count.
3
Identify Robot MM's new physical location.
Robot MM moves to Robot PP's original spot, which is stated as being 31st31^{\text{st}} from the right end.
To find Robot MM's rank from the left, we first need to isolate its exact rank from the right side.
4
Calculate Robot MM's new rank from the left end.
Rank from Left=N−(Rank from Right)+1\text{Rank from Left} = N - (\text{Rank from Right}) + 1. Therefore, Rank = 74−31+1=4474 - 31 + 1 = 44.
Subtracting the right rank from the total gives the number of robots to the left of Robot MM. Adding 1 includes Robot MM in the final positional count.

Anahtar Kavram

Positional Interchange and Total Sequence Capacity
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Konular

Order and Ranking

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