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GATE 2024 DA – Question 2

General Aptitude · Analytical Aptitude: Logical Reasoning and Deduction · 1 mark · Multiple choice

The 15 parts of the given figure are to be painted such that no two adjacent parts with shared boundaries (excluding corners) have the same color. The minimum number of colors required is

an ellipse containing a square, with a small circle at the centre divided into 3 sectors by a Y-shaped set of lines. Four lines run from the corners of the square to the circle, dividing the space between the square and the circle into 4 regions. Lines also run from the corners of the square to the ellipse, dividing the outer ring into 8 regions.
  1. 4
  2. 3
  3. 5
  4. 6

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Show answer and explanation

Correct answer: (A) 4

Explanation

The 3 sectors of the central circle all touch each other, so they need 3 different colours. Number them 1, 2 and 3. Of the 4 regions between the circle and the square, the top one touches the sectors with colours 1 and 2, the left one touches the sectors 2 and 3, and the right one touches 1 and 3. These three regions also touch each other in a chain, so they need further colours, and the bottom region, which touches only sector 3 but is next to the left and right regions, ends up needing a fourth colour. So 3 is not enough. Since any map on a plane can be coloured with 4 colours, the minimum is 4.