Non-Verbal Reasoning Notes for Competitive Exams

Non-verbal reasoning tests your ability to understand and analyse visual information such as shapes, patterns and figures, without using words. It is an important part of SSC CGL, CHSL, MTS, GD, railway (RRB NTPC, Group D), defence exams (NDA, CDS, AFCAT) and many state-level exams. In SSC papers, several marks can come from figure-based questions alone. UPSC CSAT does not focus heavily on figures, but questions on counting figures, pattern completion and spatial thinking do appear occasionally. The good news is that most non-verbal questions follow fixed rules. Once you learn these rules and practise with a timer, you can solve them faster than almost any other type of question.

Quick Facts at a Glance

• Mirror image (vertical mirror): Left and right are swapped; top and bottom stay the same.
• Water image (horizontal reflection): Top and bottom are swapped; left and right stay the same.
• Paper folding: Unfold step by step in reverse order; each fold doubles the holes.
• Embedded figures: The given shape must appear exactly, in the same size and orientation, inside the answer figure.
• Counting figures: Label every point and count systematically.

1. Mirror Images

When an object is placed in front of a vertical mirror, its left becomes right and right becomes left, but its top and bottom remain unchanged. Exams ask for the mirror image of letters, numbers, words, clocks and figures.

Letters That Look the Same in a Vertical Mirror

A, H, I, M, O, T, U, V, W, X and Y look the same in a vertical mirror (in capital letters). For example, the mirror image of "TOMATO" looks identical in shape, while "RAM" changes because R is not symmetric.

Method for Mirror Images

1. Reverse the order of characters from left to right.
2. Flip each character horizontally.
3. Check the position of small parts: dots, tails and curves must move to the opposite side.

Example: The mirror image of "BAT" written in capitals: the order becomes T A B, and B is flipped so its curves face left. Look for the option where B's bumps face left and the letters appear in reverse order.

2. Water Images

A water image is the reflection of an object in water, as if a mirror were placed horizontally below it. The top becomes the bottom, but left and right stay the same.

Letters That Look the Same in Water Image

B, C, D, E, H, I, K, O and X look the same when reflected in water (in capital letters). Numbers like 0, 3 and 8 also look the same in a water reflection.

Example: The water image of "BOX" looks the same as the original, since B, O and X are all symmetric about a horizontal line.

Tip: To compare quickly, turn the answer options upside down mentally and check whether the left-right order is unchanged. In mirror image questions, the left-right order changes; in water image questions, it does not.

3. Paper Folding and Cutting

In these questions, a square sheet of paper is folded one or more times, a hole is punched or a cut is made, and you must find how the paper looks when unfolded.

Rules

• Each fold creates a mirror line. When you unfold, the hole appears on both sides of the fold, at equal distance from the fold line.
• One fold → 2 holes; two folds → 4 holes; three folds → 8 holes (if punched through all layers).
• Unfold in reverse order: the last fold is opened first.
• Diagonal folds create holes that are reflections across the diagonal.

Example: A square sheet is folded in half vertically (left over right), then in half horizontally (top over bottom). A hole is punched near the folded corner. When unfolded, there will be 4 holes, arranged symmetrically around the centre.

4. Paper Cutting and Shape Formation

Some questions show a folded paper with a cut shape and ask which pattern appears after unfolding. Treat the cut like a hole: reflect it across each fold line. A triangular cut along a fold line becomes a diamond shape when opened.

5. Embedded Figures

An embedded figure question gives a simple figure (X) and four complex figures. You must find the complex figure in which X is hidden exactly, without rotation (unless the question permits it) and in the same size.

Method

1. Note the distinctive feature of X, such as a pointed corner, a curve or an unusual angle.
2. Look for that feature in each answer figure.
3. Trace the rest of X from that point and confirm all lines match.
4. Reject options where the figure appears rotated or resized.

6. Figure Completion and Pattern Completion

A figure is shown with a missing part, and you must choose the option that completes it. Most such figures are symmetric along vertical, horizontal or diagonal lines. Look at the opposite quarter of the figure to predict the missing part. In pattern completion, observe how lines and shapes continue across the missing region.

7. Counting Figures

Counting triangles, squares or rectangles in a complex figure is a common SSC question.

Useful Formulas

Example: A 3 × 3 grid of squares contains 1 + 4 + 9 = 14 squares. A 4 × 4 grid contains 1 + 4 + 9 + 16 = 30 squares.

Example: A grid formed by 4 horizontal and 5 vertical lines contains 4C2 × 5C2 = 6 × 10 = 60 rectangles.

Systematic Counting Method

For irregular figures, label each corner with a letter. Count shapes made of one region, then two regions, then three, and so on. Write each shape as a set of letters (like ABE) so you do not count it twice.

8. Other Non-Verbal Types

• Series of figures: Shapes rotate, add or remove elements step by step. Track one element at a time.
• Analogy of figures: Find the change between the first pair and apply it to the second.
• Odd figure out: Look for the one that does not follow the rule of rotation, count or symmetry.
• Dot situation: Find the figure where a dot can be placed in the same set of overlapping shapes.
• Cubes and dice are covered in a separate note because of their importance.

Common Mistakes to Avoid

1. Confusing mirror images with water images.
2. Forgetting to reverse the order of characters in mirror images of words.
3. Unfolding paper in the wrong order.
4. Accepting a rotated figure in embedded figure questions.
5. Counting the same triangle twice in complex figures.

Preparation Strategy

• Practise 10 questions a day from one non-verbal type, rotating through all types weekly.
• Use real paper to practise folding and punching for a few days; it builds intuition quickly.
• Keep a list of symmetric letters for mirror and water images and revise it.
• Solve previous year SSC papers to see the exact style of figures used.

Mirror and Water Images of Numbers and Clocks

Numbers behave just like letters. In a vertical mirror, 0, 1 and 8 keep their shape, while 2, 3, 4, 5, 6, 7 and 9 appear reversed. So the mirror image of "2018" is read from right to left as "8102", with 2 drawn backwards. In a water image, 0, 3 and 8 keep their shape, while 6 and 9 appear similar to each other upside down. Always draw digits clearly on your rough sheet before choosing an option.

For clocks, the mirror rule is the subtraction from 11:60 explained in the clocks chapter. For water images of clocks, the safest method is visual: imagine the clock flipped upside down so that 12 and 6 swap places while 3 and 9 stay where they are, then read the new positions of both hands. For example, a minute hand pointing at 3 still points at 3 in the water image, but a minute hand pointing at 12 now points at 6. Working visually avoids errors from memorised shortcuts that apply only in certain time ranges.

A 15-Minute Daily Routine

Spend five minutes on mirror and water images, five minutes on paper folding or embedded figures, and five minutes on counting figures. Rotate the order every day. In four weeks, you will have practised more than 400 figure questions, which is usually enough to make this section one of your highest-scoring areas in SSC and railway exams.

Related Notes

• Analogy, Classification and Odd One Out Notes
• Number and Letter Series Notes
• Direction Sense and Seating Arrangement Notes
• All Reasoning Notes

Frequently Asked Questions

What is non-verbal reasoning?

Non-verbal reasoning tests the ability to understand and analyse visual information such as shapes, figures and patterns.

What is the difference between mirror image and water image?

A mirror image swaps left and right. A water image swaps top and bottom.

Which capital letters look the same in a mirror?

A, H, I, M, O, T, U, V, W, X and Y.

Which capital letters look the same in water image?

B, C, D, E, H, I, K, O and X.

How many holes appear after two folds and one punch?

Four holes, because each fold doubles the number of holes.

How do I solve paper folding questions?

Unfold the paper in reverse order and reflect each hole across every fold line.

What is an embedded figure?

It is a simple figure hidden exactly, in the same size and orientation, inside a more complex figure.

How many squares are in a 4 × 4 grid?

There are 30 squares: 16 + 9 + 4 + 1.

How do you count rectangles in a grid?

Multiply the combinations of horizontal lines taken two at a time by vertical lines taken two at a time.

Is non-verbal reasoning asked in UPSC CSAT?

It appears only occasionally in CSAT. It is much more important in SSC, railway and defence exams.

How do I avoid double counting in figure counting?

Label every corner and write each shape as a set of letters, then count systematically.

How can I improve at non-verbal reasoning quickly?

Learn the rules for each type, practise daily with a timer and use real paper for folding questions.