Unit–IV: Introduction to Logic
1. Number Series, Coding-Decoding, and Odd Man Out
Logical reasoning tests evaluate analytical thinking and pattern identification across numeric and alphabetic data sequences.
PATTERN ANALYSIS WORKFLOW
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[ Observe Sequence ] —> [ Identify Rules / Operations ] —> [ Apply Rule / Spot Outlier ]
| Topic Area | Underlying Operational Rules | Standard Example & Solution Technique |
|---|---|---|
| Number Series | Arithmetic/Geometric differences, prime numbers, square/cube addition patterns. | Series: 2, 5, 10, 17, 26, ? Pattern: +3, +5, +7, +9, +11 Next Term: 26 + 11 = 37 |
| Coding & Decoding | Letter shifting (+n / −n), reverse alphabetical positions, matrix substitutions. | Rule: If “CAT” is coded as “3120” (A=1, B=2 …) Code: “DOG” = 4157 |
| Odd Man Out Series | Classifying items by shared mathematical properties and isolating non-conforming items. | Set: 11, 13, 15, 17, 19 Outlier: 15 (Composite number; all others are prime). |
2. Direction Sense Test
Direction problems evaluate spatial positioning based on fundamental cardinal coordinates, angle rotations, and distance calculations using basic geometry.
CARDINAL DIRECTION GRID
North (N)
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North-West (NW) | North-East (NE)
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West (W) ——————-+——————- East (E)
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South-West (SW) | South-East (SE)
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South (S)
Core Solving Principles
1. Pythagoras Theorem for Distance:
Shortest Distance (d) = √(a² + b²)
2. Turn Reference Rules:
- Right Turn: 90° Clockwise rotation.
- Left Turn: 90° Anti-clockwise rotation.
3. Shadow Dynamics:
- Sunrise (Morning): Shadows always fall towards the West.
- Sunset (Evening): Shadows always fall towards the East.
3. Seating Arrangements (Linear and Circular)
Seating arrangement puzzles test the ability to arrange individuals logically based on given positional constraints.
SEATING ARRANGEMENT TYPES
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LINEAR ARRANGEMENT CIRCULAR ARRANGEMENT
Arranging items along a single line (row/column). Arranging items around a circular table.
• Facing North: Left is West, Right is East • Facing Center: Clockwise = Left, Anti-clockwise = Right
• Facing South: Left is East, Right is West • Facing Outside: Clockwise = Right, Anti-clockwise = Left
Step-by-Step Solving Methodology
- Step 1: Identify definite statements (e.g., “A sits third to the right of B”).
- Step 2: Plot anchor positions on the layout diagram before incorporating conditional statements.
- Step 3: Use elimination to resolve secondary options (e.g., “C does not sit adjacent to D”).
4. Blood Relations
Blood relation problems test structural family hierarchy analysis and deduction.
FAMILY TREE NOTATION SYSTEM
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GENDER SYMBOLS GENERATION LEVELS RELATIONSHIP TYPES
☐ or [+] for Male Higher generation placed above Single line (—) for Siblings
○ or [−] for Female Lower generation placed below Double line (=) for Married Couples
| Standard Relation Term | Relational Description | Direct Family Lineage |
|---|---|---|
| Paternal Relations | Relatives on the Father’s side | Grandfather, Grandmother, Uncle, Aunt |
| Maternal Relations | Relatives on the Mother’s side | Maternal Uncle, Maternal Aunt, Grandfather |
| In-Law Relations | Relatives by marriage | Brother-in-law, Sister-in-law, Father-in-law |
5. Arithmetic and Geometric Progressions (AP & GP)
Progressions are ordered sequences of numbers that follow explicit algebraic laws.
PROGRESSION MODELS
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ARITHMETIC PROGRESSION (AP) GEOMETRIC PROGRESSION (GP)
Sequence with a constant common difference (d) Sequence with a constant common ratio (r)
Example: 2, 5, 8, 11 … (d = 3) Example: 3, 6, 12, 24 … (r = 2)
Key Algebraic Formulae
| Parameter | Arithmetic Progression (AP) | Geometric Progression (GP) |
|---|---|---|
| General Sequence | a, a+d, a+2d, a+3d, … | a, ar, ar², ar³, … |
| n-th Term (Tn) | Tn = a + (n − 1)d | Tn = a · rn−1 |
| Sum of n Terms (Sn) | Sn = (n/2)[2a + (n − 1)d] Sn = (n/2)(a + l) |
Sn = a(rn − 1)/(r − 1) (r > 1) Sn = a(1 − rn)/(1 − r) (r < 1) |
| Infinite Sum (S∞) | Not applicable (∞) | S∞ = a/(1 − r) (|r| < 1) |
6. Inductive and Deductive Reasoning
Reasoning methods form the foundation of logical evaluation, scientific discovery, and decision-making.
LOGICAL REASONING APPROACHES
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INDUCTIVE REASONING (Bottom-Up) DEDUCTIVE REASONING (Top-Down)
Specific Observations → Broad Generalization General Rules/Premises → Specific Conclusion
(Probable conclusions based on patterns) (Guaranteed conclusions based on valid premises)
| Feature | Inductive Reasoning | Deductive Reasoning |
|---|---|---|
| Direction of Logic | Bottom-Up (Specific to General) | Top-Down (General to Specific) |
| Certainty of Conclusion | Probable / Plausible (Can be false even with true observations) | Absolute / Certain (If premises are true, conclusion MUST be true) |
| Primary Application | Forming hypotheses, scientific research, data trends | Formal logic, mathematical proofs, legal arguments, syllogisms |
| Classic Example | “Every swan observed so far is white. Therefore, all swans are white.” | “All humans are mortal (Premise 1). Socrates is human (Premise 2). Therefore, Socrates is mortal.” |
Key Learning Summary
| Topic Area | Operational Focus |
|---|---|
| Series & Coding | Identify underlying numerical or alphabetical rules (+n, −n, ×n). |
| Direction Test | Map movements using cardinal grids and d = √(a² + b²). |
| Arrangements & Blood Relations | Use family trees and layout diagrams to systematically plot connections. |
| AP & GP | Calculate terms and sums using difference (d) and ratio (r) formulas. |
| Inductive vs. Deductive | Inductive logic generalizes from patterns; deductive logic derives definitive rules from true premises. |