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GATE 2022 BM – Question 10

General Aptitude · Spatial Aptitude: Spatial Reasoning and Visualization · 2 marks · Multiple choice

The plot shown must be divided among four families into similar shapes, possibly of different areas. Poles are equally spaced. Existing ropes R1 and R2 cannot move. What minimum number of additional straight ropes is required? One rope may pass through three collinear poles.

Diagram for GATE 2022 BM question 10
  1. 2
  2. 4
  3. 5
  4. 3

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Show answer and explanation

Correct answer: (D) 3

Explanation

Use pole spacing as one unit and the top-left pole as (0,0), with y downward. R1 ends at (2,4), R2 at (4,2). Add segments (2,4)–(4,2), (4,2)–(6,2), and (2,4)–(2,6). These produce four similar pentagons: two of linear size two and two of size four, each with one corner cut at forty-five degrees. Thus three ropes suffice, D. With only two additions the two internal rope ends cannot both join the four-region boundary arrangement of these similar plots.

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