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GATE 2023 CE (CE1) – Question 5

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

A line of symmetry is defined as a line that divides a figure into two parts in a way such that each part is a mirror image of the other part about that line.
The figure below consists of 20 unit squares arranged as shown. In addition to the given black squares, upto 5 more may be coloured black. Which one among the following options depicts the minimum number of boxes that must be coloured black to achieve two lines of symmetry? (The figure is representative)

a grid of 4 columns and 5 rows. The black squares are in row 1 (columns 2, 3), row 2 (columns 1, 4), row 4 (columns 1, 3, 4) and row 5 (columns 2, 3). The white squares are labelled a, b (row 1, columns 1 and 4), c, d (row 2, columns 2 and 3), e, f, g, h (row 3), i (row 4, column 2) and j, k (row 5, columns 1 and 4).
  1. d
  2. c, d, i
  3. c, i
  4. c, d, i, f, g

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Correct answer: (B) c, d, i

Explanation

The two lines of symmetry must be the vertical line through the middle of the grid and the horizontal line through the middle of row 3. For the vertical symmetry, row 4 has black squares in columns 3 and 4, so column 2 (i) must also be black. For the horizontal symmetry, row 4 must match row 2, but row 4 now has columns 1, 2, 3, 4 black, so row 2 needs c and d black as well. Rows 1 and 5 already match. So c, d and i are the minimum.