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.