This area checks structured representation. A small line diagram, compass sketch or Venn diagram often solves faster than mental calculation.
Core Definitions
Ranking
Standard definition: Position of an item/person in an ordered list from top/bottom/left/right.
Exam meaning: क्रममा कुनै व्यक्ति/वस्तुको स्थान।
Venn diagram
Standard definition: A diagram using circles/sets to show inclusion, exclusion and overlap.
Exam meaning: Set बीचको relation देखाउने circle diagram।
How To Think
Order problems are one-dimensional constraints. Direction problems are coordinate movement. Venn problems are set membership. Convert words into diagrams immediately.
Ranking Logic
Use formulas only after understanding orientation.
- Total = rank from top + rank from bottom – 1 for same person.
- Persons between A and B = difference of ranks – 1.
- If ranks are from opposite ends for different people, draw line when uncertain.
- For swap problems, track old and new positions separately.
Direction and Venn Logic
Compass and set drawings reduce errors.
| Topic | Representation | Key caution |
|---|---|---|
| Direction | N/E/S/W coordinate arrows | Left/right depends on facing direction |
| Ranking | Number line | Top vs bottom confusion |
| Venn | Circles and regions | At least/only/all language |
| Seating | Linear/circular diagram | Facing center/outside changes left-right |
Formulas and Rules
- Same person total count = rank from one end + rank from other end – 1.
- Between count = larger rank – smaller rank – 1 when same direction.
- Coordinate movement: East +x, West -x, North +y, South -y.
- Distance from origin = square root of x^2 + y^2 for perpendicular movement.
Step-by-Step Method
- Underline direction words: left, right, north, south, facing.
- Draw line/compass/set diagram before solving.
- Mark known positions first, then uncertain spaces.
- For Venn, fill exact-only regions before overlaps.
- Check whether question asks total, only, both or neither.
Worked Examples
- A is 7th from top and 18th from bottom. Total = 7+18-1 = 24.
- A walks 3 km east then 4 km north. Shortest distance = 5 km by 3-4-5 triangle.
- In 60 students, 35 know C, 30 know Java, 15 know both. At least one = 35+30-15 = 50. Neither = 10.
| Word | Meaning | Diagram Action |
|---|---|---|
| Only A | A but not B | A exclusive region |
| Both | Intersection | Overlap |
| At least one | Union | All covered circles |
| Neither | Outside all sets | Outer region |
Exam Point
- Use diagrams even for simple-looking questions.
- Same-person ranking formula is common.
- Direction left/right changes when person faces south or outside.
- In Venn, union = A + B – intersection.
Visual Practice
- Draw compass with coordinates.
- Draw ranking number line top-to-bottom.
- Practice two-set and three-set Venn diagrams.
- Use seating arrows for facing direction.
Common Mistakes
- Adding ranks without subtracting one.
- Confusing left and right when facing changes.
- Counting overlap twice.
- Ignoring “only” in Venn questions.
MCQ Revision
- What is total if rank top=5 and bottom=12?
- What is A union B formula?
- Which direction is opposite east?
- What does “only A” mean?
- Why draw compass?
Final Summary
- Representation is the main skill.
- Ranking uses position formulas.
- Direction is coordinate movement.
- Venn diagrams require exact set language.