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Counting Figures — Non-Verbal Reasoning Questions & Practice

108 Counting Figures questions from Non-Verbal Reasoning for competitive exams such as UPSC, Banking, SSC and Railway. Read the worked questions below, check every answer with an explanation, and track what you get wrong. का अभ्यास करें

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Counting Figures पर अभ्यास प्रश्न — उत्तर सहित

Try each question first, then open the answer. Explanations are included.

1. A square is divided into a grid of 2 x 2 equal unit squares (like a chessboard pattern). Counting squares of ALL sizes (1x1, 2x2, up to 2x2), what is the total number of squares in the figure?

उत्तर दिखाएँ

उत्तर: A

The total number of squares of all sizes in an n x n grid is 1^2 + 2^2 + ... + n^2. For n=2: 1 + 4 = 5.

2. A square is divided into a grid of 3 x 3 equal unit squares (like a chessboard pattern). Counting squares of ALL sizes (1x1, 2x2, up to 3x3), what is the total number of squares in the figure?

उत्तर दिखाएँ

उत्तर: B

The total number of squares of all sizes in an n x n grid is 1^2 + 2^2 + ... + n^2. For n=3: 1 + 4 + 9 = 14.

3. A square is divided into a grid of 4 x 4 equal unit squares (like a chessboard pattern). Counting squares of ALL sizes (1x1, 2x2, up to 4x4), what is the total number of squares in the figure?

उत्तर दिखाएँ

उत्तर: C

The total number of squares of all sizes in an n x n grid is 1^2 + 2^2 + ... + n^2. For n=4: 1 + 4 + 9 + 16 = 30.

4. A square is divided into a grid of 5 x 5 equal unit squares (like a chessboard pattern). Counting squares of ALL sizes (1x1, 2x2, up to 5x5), what is the total number of squares in the figure?

उत्तर दिखाएँ

उत्तर: D

The total number of squares of all sizes in an n x n grid is 1^2 + 2^2 + ... + n^2. For n=5: 1 + 4 + 9 + 16 + 25 = 55.

5. A square is divided into a grid of 6 x 6 equal unit squares (like a chessboard pattern). Counting squares of ALL sizes (1x1, 2x2, up to 6x6), what is the total number of squares in the figure?

उत्तर दिखाएँ

उत्तर: A

The total number of squares of all sizes in an n x n grid is 1^2 + 2^2 + ... + n^2. For n=6: 1 + 4 + 9 + 16 + 25 + 36 = 91.

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