Non-Verbal Reasoning • Mirror and water images • Paper folding/cutting • Embedded figures • Figure series and completion ________________________________________
Non-Verbal Reasoning: Full-Length Notes
Topics Covered:
Mirror and Water Images
Paper Folding/Cutting
Embedded Figures
Figure Series and Completion
1. Mirror and Water Images
A. Mirror Images
Definition:
A mirror image is the reflection of an object in a plane mirror. The image appears almost identical to the object but is reversed left-to-right (lateral inversion). The top and bottom remain the same46.
Key Points:
Left and right sides are interchanged.
Top and bottom remain unchanged.
For letters like A, H, I, M, O, T, U, V, W, X, Y, the mirror image is identical to the original3.
For clocks, to find the mirror image time, subtract the given time from 11:60 (for a vertical mirror placed at 12 o’clock position)4.
Example:
Mirror image of “DEAR” will have each letter laterally inverted.
For the word “WATER,” each letter’s mirror image is constructed, and the word is reversed as if a mirror is placed to the right3.
B. Water Images
Definition:
A water image is the reflection of an object as seen in water. It is a vertically inverted image obtained by turning the object upside down1245.
Key Points:
Top and bottom are interchanged; left and right remain the same.
The image appears as if a mirror is placed horizontally below the object14.
Water images of some words/letters are identical to the original (e.g., KICK, HIKE)3.
Example:
Water image of “STORE” is formed by inverting each letter vertically and arranging them in the same order34.
For numbers, the water image of “16892” is obtained by inverting each digit vertically3.
Difference Table:
| Aspect | Mirror Image | Water Image |
|---|---|---|
| Direction | Left-right reversal | Top-bottom inversion |
| Mirror Placed | Vertically (side) | Horizontally (bottom) |
| Example | ‘b’ → ‘d’ | ‘b’ → upside-down ‘b’ |
2. Paper Folding and Cutting
Definition:
Paper folding/cutting questions involve visualizing the result of folding a paper (once or multiple times) and then making cuts or holes. The task is to determine the final pattern when the paper is unfolded.
Key Concepts:
Single Fold: Paper is folded once and cut; the cut appears symmetrically on both sides when unfolded.
Multiple Folds: Each fold multiplies the number of symmetrical cuts or holes.
Types of Cuts: Straight, circular, triangular, etc.
Approach:
Visualize each fold.
For each cut, imagine its mirrored position on all folded layers.
Unfold the paper step by step, replicating the pattern symmetrically.
Example:
A square paper is folded in half and a triangle is cut from the folded edge. When unfolded, two triangles appear symmetrically.
If folded twice (quarter fold), one cut results in four symmetrical shapes.
3. Embedded Figures
Definition:
Embedded figure questions require identifying a simple shape hidden within a complex figure.
Key Points:
The embedded figure may be rotated or partially hidden.
The task is to match the given simple figure with its occurrence inside the complex figure.
Approach:
Focus on unique features (angles, lines, curves) of the simple figure.
Scan the complex figure for matching features.
Rotate the simple figure mentally if needed.
Example:
Given a triangle, find where it is hidden within a complex geometric design.
4. Figure Series and Completion
A. Figure Series
Definition:
A sequence of figures is given, each following a certain pattern or rule. The task is to find the next figure in the series.
Types of Patterns:
Rotation (clockwise/anticlockwise)
Addition or deletion of elements
Change in shading or shape
Movement of parts
Approach:
Observe changes from one figure to the next.
Identify the rule (rotation, addition, etc.).
Apply the rule to predict the next figure.
Example:
A square with a dot in each corner moves the dot clockwise in each step. The next figure will have the dot in the next corner.
B. Figure Completion
Definition:
A figure is partially drawn, and you must choose the option that correctly completes it.
Approach:
Analyze the symmetry and pattern of the incomplete figure.
Match the options to the missing part.
Check for continuity of lines, shapes, and patterns.
Example:
A half-completed mandala pattern is shown; choose the correct quarter from the options to complete it.
5. Quick Tips and Tricks
For mirror images, focus on left-right reversal; for water images, focus on top-bottom inversion14.
For paper folding/cutting, remember: each fold doubles the number of cuts when unfolded.
For embedded figures, look for unique angles or shapes.
For figure series, write down the observed pattern before choosing the answer.
Practice with a variety of figures to improve visualization skills.
6. Practice Resources
[LearnFrenzy: Water Images]1
[IndiaBIX: Water Images]2
[Cuemath: Mirror and Water Images]4
[SelfStudys: Mirror and Water Images]3
[Scribd: Water and Mirror Images]5
Summary:
Non-verbal reasoning tests your ability to visualize and manipulate images mentally. Mastering mirror/water images, paper folding/cutting, embedded figures, and figure series requires practice, attention to detail, and a clear understanding of symmetry and pattern rules134.
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