Analytical Reasoning Test: IQ and Logical Reasoning Questions, Tricks, and Practice

The Analytical Reasoning Test is a vital component of the Non-Verbal Reasoning section that evaluates your ability to analyze complex figures, count geometric shapes, and apply logical reasoning to visual problems. These questions test your spatial visualization, attention to detail, systematic counting ability, and analytical thinking skills. The key skill is to develop a systematic approach to counting figures and analyzing spatial relationships.

For Officer Cadet Entrance Exam preparation, mastering this topic is essential because it assesses your capacity to break down complex visual information into manageable parts and draw logical conclusions.

In this guide, we’ll explore what analytical reasoning involves in a non-verbal context, the common question types you’ll encounter, proven methods to solve them, and practical tricks to boost your speed and accuracy.

What is Analytical Reasoning in Non-Verbal Reasoning?

Analytical Reasoning in a non-verbal context refers to the ability to systematically analyze figures, count geometric shapes such as triangles, squares, rectangles, and parallelograms, and identify spatial relationships within complex diagrams. Unlike verbal analytical reasoning, which deals with statements and arguments, this version relies entirely on visual patterns and figure-based problems.

Non-verbal reasoning as a whole tests your ability to recognize patterns and relationships among shapes and symbols based on a rule. The analytical reasoning section within it covers counting of figures, figure matrices, embedded figures, and grouping of identical figures.

Example: Count the number of triangles in a given complex figure made up of intersecting lines. Rather than scanning randomly, you label the smaller unit triangles first, then work up through the larger 2-unit and 3-unit combinations, adding each size category to the running total.

What Skills Do These Questions Measure?

Analytical reasoning questions test your ability in:

• Systematic observation and analysis – working through a figure methodically rather than randomly
• Spatial visualization and mental rotation – picturing how a shape looks when rotated or reflected
• Attention to detail – catching every shape, including ones hidden in overlaps
• Pattern recognition – spotting the rule that governs a sequence of figures
• Logical and analytical thinking – breaking a complex diagram into manageable parts
• Systematic counting and categorization – tracking counts accurately across shape sizes and groups
• Speed and accuracy – solving visually dense problems within exam time limits

This topic is part of the Non-Verbal Reasoning Test in the Officer Cadet syllabus and is a high-scoring area because questions follow predictable patterns and test fundamental cognitive abilities.

Important Terms and Definitions

• Analytical reasoning (non-verbal) – the systematic analysis of visual figures to count shapes, identify patterns, and solve spatial problems
• Counting of figures – systematically counting how many of a specific shape appear in a complex figure
• Spatial visualization – the ability to mentally manipulate, rotate, and transform objects in space
• Figure matrix – a rectangular grid of figures that follow a specific rule, with one figure missing for you to identify
• Embedded figure – a simple shape hidden within a larger, more complex figure
• Grouping of identical figures – identifying figures that share common properties or belong to the same category
• Mirror image – the reflection of a figure as seen in a mirror, where left and right are reversed
• Water image – the reflection of a figure as seen in water, where top and bottom are reversed

Fundamental Concepts

Counting of Figures: Key Principles

Always count shapes systematically rather than randomly, since a structured method prevents missed or double-counted shapes. Break complex figures into simpler components, count the shapes within each, and combine the totals. Label different parts of the figure as you go so you can track exactly what’s already been counted, and stay alert for shapes that share a line or overlap with another shape, since these are the easiest to double-count.

Figure Matrix: Key Principles

Look at rows first, then columns, identifying changes such as rotation, number, shape, or shading. Figures can change in multiple ways at once — shape, count, rotation, shading, and position — so isolate one feature at a time. Whatever rule governs the pattern should apply consistently across every row and column.

Embedded Figures: Key Principles

The question figure must be an actual, integral part of the answer figure — not just something that looks superficially similar. The question figure may appear rotated at any angle within the answer options, and answer figures often contain deliberately similar shapes or lines designed to distract you from the real match.

How to Solve Analytical Reasoning Questions

Follow this step-by-step method during your exam.

Step 1: Read the Question Carefully

Identify which type of analytical reasoning question you’re facing — counting of figures, a figure matrix, embedded figures, grouping, or mirror/water images — since each requires a different approach.

Step 2: For Counting Figures, Use a Systematic Approach

Label all the smaller shapes or regions in the figure, count shapes by size category (single unit, two units, three units, and so on), add all the counts together, and verify by counting again in a different order.

Step 3: For a Figure Matrix, Analyze the Pattern

Look at rows first, then columns, identifying one feature at a time — rotation, number, shape, or shading — and apply the rule you find to determine the missing figure.

Step 4: For Embedded Figures, Look for Unique Features

Trace the outline of the small figure, look for its sharpest or most distinct angle first, and eliminate any option that doesn’t contain even a single matching angle.

Step 5: Verify Your Answer

Check that your answer makes logical sense and satisfies every condition stated in the question.

Step 6: Manage Your Time

If a question is taking too long, mark it, move on, and return later if time allows: Solve → Mark if necessary → Move on → Return later.

Types of Analytical Reasoning Questions

For Officer Cadet preparation, analytical reasoning questions may involve:

• Counting of figures – triangles, squares, rectangles, and parallelograms within a complex diagram
• Figure matrix completion – finding the missing figure that fits a row/column pattern
• Embedded figures – locating a simple shape hidden inside a larger figure
• Grouping of identical figures – sorting figures into categories based on shared properties
• Mirror images – identifying how a figure appears when reflected in a mirror
• Water images – identifying how a figure appears when reflected in water
• Cubes and dice – counting cubes in a stack or identifying opposite and hidden faces

Counting of Triangles

Example: Count the number of triangles in the given figure. Label all the smaller, single-unit triangles first, then separately count the larger 2-unit and 3-unit triangles formed by combining smaller ones, and add every size category together for the final total.

Counting of Squares

Example: Count the number of squares in the given figure. Count squares of size 1×1 first, then 2×2, then 3×3 if the figure is large enough, and add every size category together.

Counting of Rectangles and Parallelograms

Example: Count the number of parallelograms in the given figure. Identify every set of parallel lines in the figure, then count parallelograms of different sizes; for a grid with m lines in one direction and n lines in another, the total number of parallelograms equals (mC2) × (nC2).

Figure Matrix Completion

Example: Select the figure that completes the matrix. Analyze the pattern across rows and columns to identify the governing rule — rotation, addition, subtraction, or combination of elements — then apply that rule to determine the missing figure.

Embedded Figures

Example: Find the figure in which the given question figure is embedded. Trace the outline of the small figure, look for its unique angles and features, eliminate any option lacking a matching angle, and count sides to rule out shapes that simply can’t contain the target figure.

Grouping of Identical Figures

Example: Group the following figures into three classes. Identify the property each figure shares with others — such as number of sides, symmetry, or shading — group the figures accordingly, and confirm that every figure has been placed in exactly one group.

Mirror Images

Example: Select the correct mirror image of the given figure. Imagine a mirror placed vertically in front of the figure: the left and right sides reverse, while the top and bottom stay exactly where they were.

Water Images

Example: Select the correct water image of the given figure. Imagine the figure reflected in water below it: the top and bottom reverse, while the left and right sides stay exactly where they were.

Important Tricks

Trick 1: Use the Component Method for Triangles

Break the figure into smaller components, count the triangles within each component separately, and then add the totals together.

Trick 2: Use the Formula for Counting Squares

For an n×n grid of squares, the total number of squares equals 1² + 2² + 3² + … + n².

Trick 3: Use the Formula for Counting Rectangles

For a grid with m lines in one direction and n lines in another, the total number of rectangles equals (mC2) × (nC2) = [m(m−1)/2] × [n(n−1)/2].

Trick 4: Look for the Sharpest Angle First

In embedded figure questions, the rarest or sharpest angle of the small figure is usually the fastest one to spot in the answer options.

Trick 5: Eliminate Using Angles

Rule out any option that doesn’t contain at least one matching angle to the question figure.

Trick 6: Count Sides for Quick Elimination

A shape with more sides can never hide inside a shape with fewer — a pentagon can never be embedded in a quadrilateral, for instance.

Trick 7: Use the Clockwise-Corner Rule

Label the corners of the small figure and look for that same sequence of corners, in the same order, within the answer figure.

Trick 8: Trace the Outline Physically

Trace the small figure with a pen or finger directly on the page to help visualize it inside the larger figure.

Trick 9: Solve Figure Matrix Features Independently

When multiple features change at once — shape, orientation, shading, position, and count — solve for each one separately rather than trying to track them all simultaneously.

Trick 10: Use the Left-Right Rule for Mirror Images

In a mirror image, left becomes right and right becomes left, while the top and bottom remain unchanged.

Common Mistakes to Avoid

• Counting randomly — this leads to missed or double-counted shapes; always use a systematic, labeled approach
• Skipping labels — without labeling parts of the figure, it’s easy to lose track of what’s already been counted
• Forgetting larger shapes — shapes of multiple sizes are often present; count every size category, not just the smallest units
• Double-counting overlapping shapes — shapes that share a line are easy to count twice; slow down around overlaps
• Ignoring rotation in embedded figures — the question figure may appear rotated, so don’t rule out an option just because its orientation looks different
• Checking only one feature in a figure matrix — figures often change in several ways at once, so verify every feature independently before settling on an answer

Quick Solving Checklist

Before selecting your answer, use this checklist:

• Identified the type of analytical reasoning question
• Labeled parts of the figure and counted systematically (for counting questions)
• Analyzed rows and columns for the governing rule (for figure matrix questions)
• Traced the outline and looked for unique features (for embedded figures)
• Considered rotations and reflections where applicable
• Eliminated options that clearly don’t match
• Verified the answer makes logical sense
• Avoided spending too much time on one question

Practice Questions

Test yourself with real analytical reasoning questions in timed, exam-style practice sets on the Pratima Academy LMS.

Conclusion

Mastering the Analytical Reasoning Test is essential for the Nepal Army Officer Cadet Entrance Examination. Success requires systematic observation, careful counting, and logical analysis — not guesswork — across scenarios involving counting of figures, figure matrices, embedded figures, mirror and water images, and grouping of figures.

Follow this disciplined approach:

Analyze → Systematize → Count/Identify → Verify → Answer

Regular practice enhances pattern recognition, spatial awareness, speed, and accuracy — skills that matter for officers who must quickly analyze complex situations, identify patterns, and make accurate decisions under pressure.

This resource is part of the IQ and Logical Reasoning preparation series for the Nepal Army Officer Cadet exam. For structured lessons, practice banks, and mock tests, access the Non-Verbal Reasoning course on the Pratima Academy LMS.