Blood Relations; Direction Sense; Series Completion — Numbers; Series Completion — Letters

Blood Relations

4.1 Family Tree Basics

Immediate Family:

• Father / Mother → Parents
• Son / Daughter → Children
• Brother / Sister → Siblings
• Grandfather / Grandmother → Grandparents (Father's/Mother's parent)

Grandson / Granddaughter → Grandchildren

Extended Family:

• Uncle = Father's brother OR Mother's brother
• Aunt = Father's sister OR Mother's sister
• Cousin = Uncle's/Aunt's child
• Nephew = Brother's/Sister's son
• Niece = Brother's/Sister's daughter

4.2 Common Tricks and Traps

"Son/Daughter of my father's son/daughter":

• Father's son = Brother
• Father's son's son = Brother's son = Nephew (I am uncle/aunt)

Gender matters:

• If someone says "She is the only daughter of my grandmother" → She is my mother/aunt
• Context determines which

4.3 Drawing Family Tree

Always draw a tree from top (elder generation) to bottom (younger generation).

• Use ▲ for male, ⬤ for female
• Horizontal lines for marriage
• Vertical/slanted lines for parent-child

4.4 Common Relationship Patterns

4.5 Coded Blood Relations

Example: "P $ Q" means P is father of Q; "P @ Q" means P is sister of Q.

• Start by converting symbols to actual relationships
• Build the family tree step by step

4.6 Generation-wise Analysis

3-generation family problems:

• List all given relationships one by one
• Assign relative position (same gen = siblings/spouses; one level down = child)
• Count how many male/female members are there

4.7 Pointing/Introducing Relation

"The man said, 'She is the daughter of my mother's only son.'"

• Mother's only son = the man himself
• The man's daughter = the girl shown
• The girl is his daughter

Direction Sense

5.1 Compass Directions

           NORTH
             ↑
    N-W  ↖  |  ↗  N-E
             |
WEST ← ------+------- → EAST
             |
    S-W  ↙  |  ↘  S-E
             ↓
           SOUTH

Key Rules:

• Left turn from North → West
• Right turn from North → East
• 180° turn from North → South
• Sunrise → East; Sunset → West
• Shadow in morning faces West (sun in East)

Shadow in evening faces East (sun in West)

• At noon, shadow points North (in Northern hemisphere)

5.2 Distance and Final Position

After a series of movements, find:

1. Final direction person is facing
2. Distance from starting point (use Pythagoras theorem if needed)

Steps:

1. Draw all movements on paper
2. Calculate net horizontal (East-West) displacement
3. Calculate net vertical (North-South) displacement
4. Distance = √(horizontal² + vertical²)
5. Direction = based on which quadrant the final point is in

5.4 Shortcut Table for Turns

5.5 Shadow-based Directions

Problems about shadows give hints about direction:

• Person's shadow to their left in morning → Person facing South
• Person's shadow to their right in evening → Person facing North

Series Completion — Numbers

6.1 Types of Number Series

Arithmetic Series (AP)

• Common difference d is constant
• Examples: 2, 5, 8, 11, 14, ... (d=3)
• Find missing term using: Tₙ = a + (n-1)d

Geometric Series (GP)

• Common ratio r is constant
• Examples: 3, 6, 12, 24, 48, ... (r=2)
• Find missing term using: Tₙ = arⁿ⁻¹

Squares and Cubes Series

• 1, 4, 9, 16, 25, ... (perfect squares)
• 1, 8, 27, 64, 125, ... (perfect cubes)
• 1, 1, 2, 4, 7, 11, 16... (difference increases)

Fibonacci-type

• Each term = sum of previous two
• 1, 1, 2, 3, 5, 8, 13, 21, 34, ...

Mixed Series

• Even positions follow one rule, odd positions another
• e.g., 2, 10, 4, 20, 8, 40... (alternating ×2 and ×2)

6.2 Approach to Solve

Step 1: Calculate differences between consecutive terms Step 2: If differences are constant → AP series Step 3: If differences form an AP/GP → second-order series Step 4: Check ratios if differences aren't meaningful Step 5: Look for alternating patterns

6.3 Common Series Patterns

Series Completion — Letters

7.1 Letter Series Patterns

Identify how letters change position in the alphabet.

Common Patterns:

• +1 position: A, B, C, D, E...
• +2 positions: A, C, E, G, I...
• +3 positions: A, D, G, J, M...
• Skip patterns: AB, DE, GH, JK...
• Reverse: Z, Y, X, W, V...

7.2 Mixed Letter-Number Series

Combination of letters and numbers:

• A2, B4, C6, D8... (letter +1, number +2)
• Z1, Y2, X3, W4... (letter reverse, number +1)

7.3 Group Patterns in Letter Series

Series given in 2-3 letter groups:

• ACE, FHJ, KMO... → every 5th letter skipped, +5 each time
• BEH, KNQ, TWZ → each group is +3 internal, +3 between groups

7.4 Dictionary Order

Arranging words in alphabetical order:

1. Compare letter by letter
2. First difference determines order
3. If all letters same up to one word's length → shorter comes first

Step-by-step for 'Spruce, Spume, Spree, Spurt, Sprawl':

• All start with 'Sp'
• 3rd letter: r (Spruce, Spree, Sprawl, Spurt) vs u (Spume)
• Among Spr...: Sprawl < Spree < Spruce < Sprut
• Order: Sprawl, Spree, Spruce, Spurt, Spume → 5,3,1,4,2