Non-Verbal Reasoning

What you'll learn

• Identify the pattern in a series of shapes and select the next figure
• Find the correct mirror image of a given figure
• Locate a smaller shape hidden within a larger complex figure
• Predict the pattern of holes after a paper is folded and punched

Key concepts

Type 1 — Figure Series Completion

A series of figures follows a visual rule. You must identify what changes from figure to figure and select the next one.

Common patterns to check:

Worked Example: Step 1: Square with one dot in top-left corner. Step 2: Square with one dot in top-right corner. Step 3: Square with one dot in bottom-right corner. Pattern: Dot moves clockwise, one corner at a time. Next (Step 4): Dot in bottom-left corner.

Tip: Look at ONE element at a time (position, number, shading, orientation). Do not try to process all elements simultaneously.

Type 2 — Mirror Images

A mirror image is the reflection of a figure as seen in a vertical mirror placed to its right.

Key rules:

1. Left and right are swapped; top and bottom stay the same.
2. Letters and numbers flip horizontally: b becomes d; p becomes q.
3. Shading and internal markings also flip left-right.

Common mirror image pairs:

Worked Example: Original figure: A triangle pointing right with a dot on its left side. Mirror image: Triangle pointing left with a dot on its right side.

Trap: The answer choices often differ only slightly (dot on wrong side, direction slightly off). Trace the left-right swap carefully for every element.

Water Images

A water image is the reflection of a figure as seen in a horizontal mirror placed below it.

• Top and bottom are swapped; left and right stay the same.
• A letter like A becomes an upside-down A; T becomes ⊥.

Type 3 — Embedded Figures

A small shape (the "key figure") is hidden inside a larger, more complex figure. You must identify which option contains the key figure.

How to find embedded figures:

1. Study the key figure — count its sides, note angles, mark distinctive features.
2. In the complex figure, trace lines that could form the key figure.
3. Check that the traced shape uses existing lines only — you cannot add new lines.

Worked Example: Key figure: A right-angled triangle. Complex figure: A large rectangle divided by diagonal lines.

Look for a right-angle corner + two sides meeting at that angle within the complex figure. The top-right section of the rectangle, when cut by one diagonal, forms a right-angled triangle. → Key figure IS embedded.

Strategy: Rotate your mental image of the key figure (0°, 90°, 180°, 270°) — it may appear rotated inside the complex figure.

Type 4 — Paper Folding and Hole Punching

A square sheet of paper is folded one or more times, then a hole is punched. When unfolded, how many holes appear and where?

Rules:

1. Each fold reflects the punched holes across the fold line.
2. If folded once: 2 holes when unfolded (1 punch + its reflection).
3. If folded twice: 4 holes (each fold doubles the count).
4. If folded three times: 8 holes.

Worked Example: Step 1: Square paper. Step 2: Fold in half vertically (left half folds over right half). Step 3: Punch one hole in the upper-right area. When unfolded: The hole appears once on the right half (original punch) and once on the left half (reflection) → 2 holes, symmetrical about the vertical fold line.

Two-fold worked example: Fold 1: Fold in half vertically. Fold 2: Fold the result in half horizontally. Punch: One hole in the center of the folded paper. Unfold: 4 holes, one in each quadrant.

Tip: Draw the fold lines. After each fold, ask: "Where does this hole reflect to?" Reflect across the fold line to find the new hole position.

General Non-Verbal Strategy

1. Isolate one feature at a time (shape, position, shading, size).
2. Name the rule in words before looking at answer choices.
3. Eliminate wrong options — often 2–3 can be ruled out quickly.
4. Mentally manipulate (rotate/flip) rather than guessing by look.

Quick check

1. In a figure series, a circle gains one extra dot each step: 1 dot, 2 dots, 3 dots. What comes next?
2. What is the mirror image of the letter "S"?
3. If paper is folded twice (once vertically, once horizontally) and one hole is punched, how many holes appear when fully unfolded?
4. In embedded figures, can you draw extra lines to find the key figure? Why or why not?
5. A square rotates 90° clockwise each step. After 4 steps, what is its orientation compared to the start?

Open the Practice tab for graded questions on Non-Verbal Reasoning.