Examkin

Question

Difficulty: HardSeating Arrangement

Six executives (K, L, M, N, O, and P) are seated around an equilateral triangular table. Three of them sit at the three corners, facing the center of the table. The other three sit exactly at the midpoints of the three sides, facing outward (away from the center).

Based on the following conditions, select all statements that are true regarding their final seating positions:

1. M sits at the midpoint of one of the sides.
2. N sits third to the right of M.
3. P sits second to the left of N.
4. O sits to the immediate right of P.
5. K is not an immediate neighbor of M.

  1. O sits exactly between N and P.Answer
  2. K sits second to the left of O.Answer
  3. C
    L sits to the immediate left of M.
  4. D
    N sits second to the right of L.

Answer

The correct statements are that O sits exactly between N and P, and K sits second to the left of O.
Based on the verified seating chart, N is at the top corner and P is at the bottom-right corner, leaving the right midpoint exactly between them for O. Furthermore, O is at the right midpoint facing outward; moving two spaces to O's left (counter-clockwise) leads to K at the left midpoint.

Step-by-Step Solution

1
Determine the left/right orientations based on facing direction.
For corner seats (facing IN), Left is Clockwise and Right is Counter-Clockwise. For midpoint seats (facing OUT), Left is Counter-Clockwise and Right is Clockwise.
Establishing relative direction mapping is essential before placing any individuals in mixed-facing geometry.
2
Place M and locate N.
Assume M sits at the bottom midpoint (facing out). Since M's right is clockwise, moving three positions clockwise places N at the top corner (facing in).
Condition 1 and 2 give a direct relationship between a midpoint and a corner.
3
Locate P based on N's position.
N is at a corner facing in, so N's left is clockwise. Moving two positions clockwise from the top corner places P at the bottom-right corner (facing in).
Condition 3 connects N to P deterministically.
4
Locate O relative to P.
P faces in, so P's right is counter-clockwise. Moving one position counter-clockwise from P places O at the right midpoint (facing out).
Condition 4 uses P's position to place O.
5
Place K and L using the negative condition.
The remaining seats are the left midpoint and the bottom-left corner. M is at the bottom midpoint. K cannot be M's neighbor, so K must take the left midpoint (facing out). L takes the remaining bottom-left corner (facing in).
Condition 5 eliminates the only other open spot for K, completing the seating chart.

Key Concept

Positional Mapping in Mixed-Orientation Polygons
Rate this question

Topics

Seating Arrangement

More questions from this topic