A sequence of figures shows a square being divided: 1st figure has 1 square, 2nd has 4 squares (2×2 grid), 3rd has 9 squares (3×3 grid). The number of internal line segments (not boundary) in the 5th figure is:

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EEJ MAIN Aptitude QUESTION #10937

Question 1

A sequence of figures shows a square being divided: 1st figure has 1 square, 2nd has 4 squares (2×2 grid), 3rd has 9 squares (3×3 grid). The number of internal line segments (not boundary) in the 5th figure is:

40✔️
32
36
24

Correct Answer Explanation

In an \(n \times n\ grid:

Horizontal internal lines: \((n-1)\ interior rows, each with \(n\ segments = \(n(n-1)\

Vertical internal lines: Similarly \(n(n-1)\

Total internal segments = \(2n(n-1)\

For 5th figure (\(n=5\): Internal segments = \(2 \times 5 \times 4 = 40\

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