Counting Figures Practice Questions with Detailed Solutions – Level 1

Counting Figures Level 1 Reasoning Practice Quiz for Beginners

Counting Figures Level 1 is a beginner logical reasoning set for students starting non-verbal reasoning. It covers counting triangles, squares and rectangles in a figure and finding the minimum number of straight lines needed to draw it. Aptitude360 gives a worked solution for every question that shows the count step by step.

What the Level 1 counting figures questions test

• Counting every triangle in a given figure
• Counting squares of all sizes
• Counting rectangles with squares included in the total
• Finding the minimum number of straight lines needed to draw a figure

Basic counting formulas for regular figures

• Triangle with base cut into \( n \) parts by lines from the apex: \( \dfrac{n(n+1)}{2} \)
• Squares in an \( n \times n \) grid: \( \dfrac{n(n+1)(2n+1)}{6} \)
• Rectangles in an \( m \times n \) grid: \( \dfrac{m(m+1)n(n+1)}{4} \)

Revision tips for counting figures at the basic stage

• Label every corner and intersection with a letter before you start counting
• Count shapes by size: single pieces first, then shapes made of two, three or more pieces
• Write each shape by its corner letters so that none is counted twice
• Use a formula only when the figure is a clean grid or a fanned triangle

Who should start with this set

Aspirants who are new to counting figures can use it to learn a systematic counting method before moving on to more crowded figures.