Non-verbal reasoning uses figures, letters and shapes instead of words. Questions ask you to continue a figure series, find a mirror or water image, count shapes, or imagine paper being folded and punched. You do not need drawing skill. You need a few rules that tell you exactly what changes and what stays the same. This note gives those rules with examples for the Lok Sewa mental ability section.
1. Figure series
In a figure series each picture changes from the one before by a fixed rule. Check one change at a time.
- Rotation: the figure turns by a fixed angle, often 45° or 90°, clockwise or anticlockwise.
- Adding or removing: one line, dot or small shape is added or removed each step.
- Moving position: a small element moves around the corners of a square, one corner each step.
- Alternating: two different changes take turns, so compare figures 1, 3, 5 and figures 2, 4.
Remember: 45° is one-eighth of a full turn and 90° is one quarter. Eight steps of 45° bring a figure back to where it started.
2. Mirror images
A mirror placed on the right side of a figure swaps left and right but keeps top and bottom the same. Letters that look the same in such a mirror are those with a vertical line of symmetry:
A, H, I, M, O, T, U, V, W, X, Y
So the mirror image of the word TOM reads the same letters in reverse order, written as MOT, and each letter keeps its shape. A word like BAT changes, because B is not symmetric from left to right.
Mirror time on a clock: if a clock seen in a mirror shows a certain time, the real time is 11:60 minus the mirror time. For example, a mirror time of 3:15 means the real time is 11:60 − 3:15 = 8:45.
3. Water images
A water image is a reflection in water below the figure. It swaps top and bottom but keeps left and right the same. Letters that look the same in water have a horizontal line of symmetry:
B, C, D, E, H, I, K, O, X
Letters such as H, I, O and X look the same in both a mirror and water because they are symmetric both ways.
4. Paper folding and punching
When a sheet is folded and then punched, the hole goes through every layer. When the sheet is opened, each layer shows a hole.
| Folds before punching | Layers | Holes after opening (one punch) |
|---|---|---|
| Folded once (in half) | 2 | 2 |
| Folded twice (in quarters) | 4 | 4 |
| Folded three times | 8 | 8 |
The holes appear as mirror images across each fold line. If the punch is near the fold, the opened holes are near the centre line; if it is near the edge, they are near the edges.
5. Counting figures
Counting triangles or squares in a figure is easy if you count in an organised way: first single small shapes, then shapes made of two parts, then three, and so on.
- A triangle with lines from the top to the base: if the base is divided into n parts, the number of triangles is n × (n + 1) ÷ 2. With 3 parts, 3 × 4 ÷ 2 = 6.
- A square divided by its two diagonals has 8 triangles: 4 small ones and 4 made of two small ones.
- A 2 × 2 grid of squares has 5 squares: 4 small and 1 large.
- A 3 × 3 grid has 9 + 4 + 1 = 14 squares.
6. Dice
On a standard die the numbers on opposite faces add up to 7: 1 is opposite 6, 2 is opposite 5 and 3 is opposite 4. Two faces that are shown next to each other in a picture can never be opposite. When two pictures of the same die share one face, the faces that move around it tell you which numbers are opposite.
7. Common traps
- In mirror questions, both the order of letters and the shape of each letter change.
- Do not mix up mirror (left-right) and water (top-bottom) images.
- In rotation series, check whether the turn is clockwise or anticlockwise.
- When counting shapes, list them by size so you do not count any twice.
📌 Key points to remember
- Figure series: check rotation, adding, moving and alternating changes.
- Mirror image swaps left and right; water image swaps top and bottom.
- Mirror-symmetric letters: A H I M O T U V W X Y.
- Water-symmetric letters: B C D E H I K O X.
- Real time from a mirror clock = 11:60 − mirror time.
- One punch through k layers gives k holes when opened.
- Triangles with n base parts = n × (n + 1) ÷ 2.
- Opposite faces of a standard die add up to 7.
Test yourself: Non-verbal Reasoning
50 questions on Figure series, Paper folding and punching and Common traps. Each attempt picks 25 at random.