GATE CS 2022 Q.10: Spatial Aptitude

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.

Plot of land with equally spaced poles on a 7 by 7 grid (top-right and bottom-left corner poles absent). The boundary runs along the top row from the left corner to the sixth pole, cuts diagonally to the right column's second pole, down the right column, along the bottom row to its second pole, diagonally to the left column's sixth pole and up the left column. Rope R2 runs vertically from the fifth pole of the top row down two spacings; rope R1 runs horizontally from the fifth pole of the left column two spacings to the right.

Official answer and solution

Official answer: D
From: Official GATE 2022 answer key

Solution

Find the minimum number of straight line segments required to partition the grid into four similar polygonal plots.

The $4 \times 4$ grid contains two fixed ropes $R_1$ and $R_2$ . To divide the land among four families, the interior must be partitioned into 4 mutually similar regions.

With 1 or 2 additional ropes, the geometry of $R_1$ and $R_2$ does not permit partitioning into 4 similar regions because each rope can only span poles along straight lines, and 2 additional lines cannot create the required four similar polygons given the asymmetry of $R_1$ and $R_2$ .

Placing exactly 3 additional straight ropes through collinear poles successfully partitions the area into four similar triangular or quadrilateral sub-plots. Hence, the minimum number of additional ropes needed is 3.

Final answer

Option (D)

Common trap

Guessing 2 ropes without verifying that the resulting four partitioned sub-plots must be mutually similar in shape.

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper: GATE 2022 Computer Science and Information Technology (CS)
Question: 10 of 65
Section: General Aptitude

Report an error in this question

GATE questions are the work of the organising institutes. This site is independent and is not affiliated with them.

Question

Solution

Source