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Difficulty: HardOrder and Ranking

In a single line of applicants waiting for an interview, Oliver is positioned 34th34^{\text{th}} from the front and Maya is positioned 41st41^{\text{st}} from the back. There are exactly 1515 applicants standing between them. If the total number of applicants in the line is the absolute minimum possible to satisfy these conditions, what is the position of the applicant standing exactly halfway between Oliver and Maya, counting from the front of the line?

  1. 26th26^{\text{th}}Answer
  2. B
    27th27^{\text{th}}
  3. C
    33rd33^{\text{rd}}
  4. D
    42nd42^{\text{nd}}

Answer

The applicant standing exactly halfway between them is in the 26th26^{\text{th}} position from the front.
To find the minimum possible number of people in the line, the positions of Oliver and Maya must overlap (Maya is closer to the front than Oliver). Since Oliver is 34th34^{\text{th}} from the front and there are 1515 people between them, Maya's position from the front is 34−15−1=18th34 - 15 - 1 = 18^{\text{th}}. The person exactly in the middle of the 1515 people between them is the 8th8^{\text{th}} person after Maya. Therefore, their position from the front is 18+8=26th18 + 8 = 26^{\text{th}}.

Step-by-Step Solution

1
Identify the arrangement type required for the minimum total number of applicants.
An overlapping arrangement must be used, meaning Maya is standing ahead of Oliver in the line.
If Oliver is ahead of Maya, the total number of applicants maximizes. For the minimum capacity, they must cross over so their positional counts overlap.
2
Calculate Maya's exact position from the front of the line.
Maya is 18th18^{\text{th}} from the front.
Oliver is 34th34^{\text{th}}. Since Maya is ahead of him with 1515 people in between, Maya's position is 34−15 (people between)−1 (Oliver)=18th34 - 15 \text{ (people between)} - 1 \text{ (Oliver)} = 18^{\text{th}} from the front.
3
Determine the relative position of the middle applicant between Oliver and Maya.
The middle applicant is exactly 88 positions after Maya.
There are 1515 applicants between them. The exact middle of a 1515-person gap is the 8th8^{\text{th}} person (77 people on one side, the middle person, and 77 people on the other side).
4
Calculate the middle applicant's absolute position from the front.
18+8=26th18 + 8 = 26^{\text{th}} position from the front.
Adding the relative 88-position offset to Maya's starting position of 18th18^{\text{th}} from the front yields the final answer.

Key Concept

Overlapping Minimum Capacity in Linear Ranking
Estimated Time:2m 0s
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Topics

Order and Ranking

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