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GATE 2022 EC – Question 5

General Aptitude · Spatial Aptitude: Spatial Reasoning and Visualization · 1 mark · Multiple choice

An art gallery engages a security guard to ensure that the items displayed are protected. The diagram below represents the plan of the gallery where the boundary walls are opaque. The location the security guard posted is identified such that all the inner space (shaded region in the plan) of the gallery is within the line of sight of the security guard.

If the security guard does not move around the posted location and has a $360^\circ$ view, which one of the following correctly represents the set of ALL possible locations among the locations P, Q, R and S, where the security guard can be posted to watch over the entire inner space of the gallery.

Diagram for GATE 2022 EC question 5
  1. P and Q
  2. Q
  3. Q and S
  4. R and S

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Show answer and explanation

Correct answer: (C) Q and S

Explanation

The gallery is a V-shaped (chevron) polygon with one reflex vertex at the notch. A guard sees the whole gallery only from the "kernel", the region on the inner side of every wall. That region is the stem below the notch, which contains Q and S. From P (in the left arm) the far end of the right arm is hidden behind the notch, and likewise R cannot see the left arm.