GATE CS 2022 Set 1 — Question 10
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General Aptitude → Quantitative Aptitude → 2D & 3D Patterns
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Question
A plot of land must be divided between four families. They want their individual plots to be similar in shape, not necessarily equal in area. The land has equally spaced poles, marked as dots in the below figure. Two ropes, R1 and R2, are already present and cannot be moved.What is the least number of additional straight ropes needed to create the desired plots? A single rope can pass through three poles that are aligned in a straight line.
Correct answer
(D) 3
Solution
The problem asks for the minimum number of additional straight ropes to divide the land into four plots of similar shape. The existing shape is a square with a corner removed (an L-shape) formed by a grid of dots. The existing ropes R1 and R2 partially divide the area.To divide an L-shaped region into 4 smaller similar L-shaped regions, we typically need to add lines that partition the central area and extend to the boundaries. By adding 3 additional ropes, we can complete the division into 4 identical smaller L-shapes.
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