In a row of 10 people, M is 5th from the left end and O is 3rd from the right…

2023

In a row of 10 people, M is 5th from the left end and O is 3rd from the right end. How many persons are there between M and O?

  1. A.

    2

  2. B.

    3

  3. C.

    1

  4. D.

    None

Show answer & explanation

Correct answer: A

For a single row of n people, a person's position counted from the left end and that same person's position counted from the right end always satisfy: (position from left) + (position from right) = n + 1. The number of people seated strictly between two people whose positions (from the same end) are known equals the difference between the larger and smaller position, minus 1 -- the two boundary people themselves are never counted as being "between".

  1. The row has n = 10 people in total. M's position from the left end is 5.

  2. O's position from the right end is 3, so O's position from the left end = 10 + 1 - 3 = 8.

  3. The number of people strictly between position 5 and position 8 = 8 - 5 - 1 = 2.

Laying the row out explicitly as _ _ _ _ M _ _ O _ _ (seats 1 to 10) confirms M at seat 5 and O at seat 8, with exactly two people -- at seats 6 and 7 -- sitting between them.

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