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📗 Nayab Subba syllabus: Paper I, General Mental Ability, Unit 2.3 · Open the full Nayab Subba course
Unit 2.3 (non-verbal reasoning) includes series, analogy, classification, mirror and water images (see Non-Verbal Reasoning) and the types below.
1. Logical Venn diagrams
Circles show how groups are related.
| Relation | Diagram | Example |
|---|---|---|
| One group fully inside another | Circle inside circle | Kathmandu ⊂ Nepal ⊂ Asia (three circles one inside another) |
| Two separate groups inside a bigger group | Two separate circles inside a big circle | Dogs and Cats inside Animals |
| Two groups that overlap | Two intersecting circles | Teachers and Women (some teachers are women) |
| Groups with nothing in common | Separate circles | Chairs and Rivers |
| Two overlapping groups inside a third | Two intersecting circles inside a big circle | Doctors and Women inside Human beings |
- Steps: take the biggest group first, then check which groups are inside, which overlap, which are separate.
- In number questions on Venn diagrams, total = A + B − (A and B). If 30 like tea, 20 like coffee and 10 like both, people who like at least one = 30 + 20 − 10 = 40.
2. Counting figures
- Squares in an n × n grid: 1² + 2² + … + n². 2 × 2 grid → 1 + 4 = 5; 3 × 3 → 14; 4 × 4 → 30.
- Rectangles (including squares) in an m × n grid: [m(m+1)/2] × [n(n+1)/2]. A 2 × 2 grid → 3 × 3 = 9.
- Triangles formed when lines are drawn from the top corner of a triangle to its base, dividing the base into k parts: k(k+1)/2. Base in 3 parts → 6 triangles.
- Method for any figure: label all points with letters, count the smallest shapes first, then shapes made of 2, 3, … parts. Write them down to avoid double counting.
3. Embedded (hidden) figures
- A simple figure is hidden inside a complex figure; find the option that contains it in the same size and the same orientation (not rotated, unless the question allows).
- Trace the outline of the simple figure with your eye from one corner.
4. Dot situation
- A figure has one or more dots placed in certain regions (for example, inside the circle and the triangle but outside the square).
- Find the option where a dot can be placed so that it satisfies exactly the same conditions.
- Write the condition for each dot in words first, then check each option.
5. Figure rotation and position change (चित्रको स्थानान्तरण)
- Clockwise: the direction in which clock hands move; anticlockwise is the opposite.
- A 90° clockwise turn moves the top to the right side; 180° turns the figure upside down; 360° brings it back to the start.
- Mirror image: left and right are swapped (lateral inversion). Water image: top and bottom are swapped.
6. Forming triangles and squares
- Choose the pieces that together make a complete square or triangle without gaps or overlaps.
- Match the edges and angles of the pieces; the total area of the pieces must equal the area of the shape.
7. Question types and tips
| Type | Tip |
|---|---|
| Series | Look for rotation, addition or removal of a part in each step |
| Mirror image | Left and right swap; top and bottom stay |
| Water image | Top and bottom swap; left and right stay |
| Paper folding and cutting | Unfold step by step; holes repeat on both sides of each fold |
| Odd one out | Count lines, sides, dots or direction of rotation |
| Embedded figure | Look for the exact shape and size inside the complex figure |
8. Common mistakes
- Mixing up mirror and water images.
- Missing a small change such as a dot or shaded part.
- Spending too long on one figure.
9. How this topic is asked in the exam
Loksewa aptitude papers include figure series, analogy, odd one out, mirror and water images, and paper folding. Practise timed sets so that each question takes under a minute.
📌 Key points to remember
- Venn: inside, overlapping, separate; total = A + B − both.
- Squares in n × n grid = 1² + 2² + … + n² (2×2 = 5, 3×3 = 14, 4×4 = 30).
- Rectangles in m × n grid = m(m+1)/2 × n(n+1)/2; triangles with base in k parts = k(k+1)/2.
- Embedded figure: same size and orientation; dot situation: same conditions for each dot.
- Mirror image swaps left–right; water image swaps top–bottom.
📝 Quiz
Test yourself: Non-Verbal Reasoning
52 questions check what you read about Logical Venn diagrams, Dot situation and Forming triangles and squares. Each attempt picks 25 at random.
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