LOGICAL REASONING – QUICK REVISION NOTES
(Tailored for JKSSB Forester Exam – Section D)
1. WHAT IS LOGICAL REASONING?
- Definition: The ability to analyse information, identify patterns, draw valid conclusions, and solve problems using structured thinking.
- Why it matters in the exam: Section D tests speed, accuracy, and the ability to handle 5‑10 minute puzzles without external aids.
- Core skill set: Observation → Classification → Inference → Elimination → Answer selection.
2. BASIC BUILDING BLOCKS | Concept | What it means | Typical exam form |
| ——— | ————— | ——————- |
| Statement | A declarative sentence that can be true or false. | “All lions are mammals.” |
| Premise | A statement used as evidence for an inference. | Premise 1: “All lions are mammals.” |
| Conclusion | The proposition that follows (or may follow) from premises. | Conclusion: “Some mammals are lions.” |
| Assumption | An unstated premise that must be true for the argument to hold. | “If the forest is protected, wildlife will thrive.” (Assumes protection → thriving) |
| Inference | A logical step derived from one or more statements. | From “If it rains, the ground gets wet” and “It is raining” → “Ground is wet.” |
| Syllogism | Two premises leading to a conclusion (categorical). | All A are B; All B are C → All A are C. |
| Venn Diagram | Visual tool to test categorical relationships. | Overlapping circles for “Some”, separate for “No”. |
3. CATEGORICAL SYLLOGISM – QUICK REFERENCE
| Type of Premise | Symbolic Form | Meaning | Conversion Rules* |
|---|---|---|---|
| Universal Affirmative (A) | All S are P | Every S belongs to P. | A → I (Some S are P) ; A → ¬E (No S are P) is invalid. |
| Universal Negative (E) | No S are P | No S belongs to P. | E → O (Some S are not P) ; E → ¬A (All S are P) is invalid. |
| Particular Affirmative (I) | Some S are P | At least one S is in P. | I → ¬E (No S are P) is invalid; I → ¬A (All S are P) is invalid. |
| Particular Negative (O) | Some S are not P | At least one S is outside P. | O → ¬I (Some S are P) is invalid; O → ¬E (No S are P) is invalid. |
\*Only valid immediate inferences are shown; the rest lead to fallacies.
Mnemonics for Mood & Figure – MOOD (type of premises): All, Eno, Isome, Osome‑not.
- FIGURE (position of middle term):
| Figure | Premise‑1 | Premise‑2 | Conclusion |
|---|---|---|---|
| 1st | M‑P | S‑M | S‑P |
| 2nd | P‑M | S‑M | S‑P |
| 3rd | M‑P | M‑S | S‑P |
| 4th | P‑M | M‑S | S‑P |
Memory tip: “All Elephants In Orange Jelly” → A‑E‑I‑O (mood) and 1‑2‑3‑4 (figure) follow the same order as the letters.
Quick Syllogism Checklist
- Identify three terms (major, minor, middle).
- Ensure the middle term is distributed at least once. 3. No term may be distributed in the conclusion if it wasn’t distributed in the premises.
- If one premise is negative, the conclusion must be negative. 5. If both premises are affirmative, the conclusion must be affirmative.
- At most one particular premise → conclusion can be particular; two particular premises → no valid conclusion.
4. SEATING ARRANGEMENT
| Sub‑type | Typical Clues | Solving Strategy |
|---|---|---|
| Linear (Row) | “A sits third to the left of B”, “C is not at any end”. | Draw a blank line, place fixed positions first, then use relative clues. |
| Circular (Round Table) | “D is opposite E”, “F sits immediate right of G”. | Mark the centre, fix one person as reference (usually the first mentioned), then place others clockwise/anticlockwise. |
| Square/Rectangular | “Persons at corners face centre”, “Persons at sides face outward”. | Treat each side as a mini‑linear arrangement; note facing direction for left/right interpretation. |
| Complex (Multiple Rows/Tables) | Combination of above with “Group 1 sits in Row 1, Group 2 in Row 2”. | Solve each group separately, then interlock using cross‑group clues. |
Key Points to Remember – Left/Right depends on the direction the person is facing (unless stated “from your perspective”).
- Immediate neighbour = directly adjacent, no one in between. – Opposite in a circle = half the total seats away.
- Not at ends eliminates the two extreme positions in a linear row.
- Use elimination: If a position cannot satisfy a clue, strike it out.
- Draw a diagram after every 2‑3 clues; re‑evaluate consistency.
Mnemonic: Left‑Right Opposite Immediate Neighbour → “L R O I N” (think of “Loin” – a cut of meat, easy to recall).
5. BLOOD RELATIONS
| Symbol | Meaning |
|---|---|
| Father (F) | Male parent |
| Mother (M) | Female parent |
| Son (S) | Male child |
| Daughter (D) | Female child |
| Brother (Br) | Male sibling |
| Sister (Si) | Female sibling |
| Husband (H) | Male spouse |
| Wife (W) | Female spouse |
| Grandfather (GF) | Father’s father / Mother’s father |
| Grandmother (GM) | Father’s mother / Mother’s mother |
| Uncle (U) | Brother of parent |
| Aunt (A) | Sister of parent |
| Cousin (C) | Child of uncle/aunt |
Core Rules 1. Generation Gap: Each step up/down the tree changes generation by ±1.
- Gender Clues: “He”, “his”, “himself” → male; “She”, “her”, “herself” → female.
- Marital Links: Husband ↔ Wife are always of opposite gender and same generation.
- Blood vs. In‑law: “Son‑in‑law” = husband of one’s daughter; “Brother‑in‑law” = husband of one’s sister or brother of one’s spouse.
- Never assume: Unless explicitly stated, avoid assuming sibling relationships from shared parents only if gender is unknown.
Solving Technique – Step 1: Identify the reference person (the one whose relation is asked).
- Step 2: Write down all direct relations given (e.g., “X is the father of Y”).
- Step 3: Build a family tree upward/downward using the reference as root. – Step 4: Apply gender and marriage constraints.
- Step 5: Answer the query by tracing the shortest path.
Mnemonic: Father Mother Son Daughter Brother Sister Husband Wife → “FMSDB SHW” (pronounce “fizz‑dub shwoo”). Helps recall the six core nuclear relations.
6. DIRECTION SENSE
| Concept | Symbol / Rule |
|---|---|
| Cardinal Points | N (North), S (South), E (East), W (West). |
| Inter‑cardinal | NE, NW, SE, SW (45°). |
| Turns | Left = 90° anticlockwise; Right = 90° clockwise; U‑turn = 180°. |
| Opposite Direction | N↔S, E↔W, NE↔SW, NW↔SE. |
| Distance | Usually given in metres/kilometres; use Pythagoras only when a right‑angled triangle is formed. |
| Shadow | Morning sun → shadow points West; Evening sun → shadow points East (in India). Noon sun → negligible shadow. |
Solving Steps
- Draw a quick sketch (a small cross for N‑S‑E‑W).
- Mark the starting point and direction faced. 3. Apply each instruction sequentially (turn → move).
- Keep track of final coordinates (x, y) or use a vector sum.
- Answer: direction from start to end, or distance using √(Δx²+Δy²).
Mnemonic: Never Eat Soggy Waffles → N‑E‑S‑W (clockwise). For anticlockwise, reverse: We Stick Every Night → W‑S‑E‑N.
7. CODING‑DECODING
| Type | Typical Pattern | Trick |
|---|---|---|
| Letter Shift | Each letter replaced by another (e.g., A→D, B→E). | Find constant shift (±n). Use alphabet positions (A=1,…Z=26). |
| Opposite Letter | A↔Z, B↔Y, … (Atbash). | Sum of positions = 27. |
| Number Coding | Letters replaced by their place values or vice‑versa. | Convert letter→number or number→letter. |
| Symbol/Number Substitution | Specific symbols stand for letters/numbers. | Build a key from given examples. |
| Jumbled Coding | Letters of a word are rearranged according to a rule (e.g., reverse, skip‑one). | Identify pattern: reversal, alternating, etc. |
| Matrix Coding | Letters placed in a grid; code given as row‑column numbers. | Locate letter in matrix, note coordinates. |
Solving Approach
- Collect at least two clear examples (word → code).
- Identify the operation (shift, reverse, opposite, etc.). 3. Test the rule on a third example if given.
- Apply to the query word/number.
- Check options – eliminate those that violate any observed rule.
Mnemonic: Shift Opposite Reverse Jumble Matrix → “S O R J M” (think of “SORMJ” – a fantasy creature). Helps recall the five main families.
8. INPUT‑OUTPUT (Sequential Logic)
| Step | What to Look For |
|---|---|
| Identify the operation | Is it arithmetic (+,‑,×,÷), logical (AND, OR, NOT), or positional (swap, shift)? |
| Check for pattern repetition | Does the same operation apply every step, or does it alternate? |
| Track invariants | Some elements may stay unchanged (e.g., first letter, sum of digits). |
| Use elimination | If a step fails for an option, discard it. |
| Draw a table | Input → Step1 → Step2 → … → Output. Visualizing helps spot the rule. |
Common Types
- Addition/Subtraction of a constant (e.g., +3 each step).
- Multiplication/Division (e.g., ×2).
- Digit rearrangement (e.g., last digit to front).
- Letter‑number conversion (e.g., A=1, then add 2).
- Combined operations (e.g., shift letters then add numbers to each).
Tip: When stuck, write down the difference between consecutive outputs; a constant difference hints at additive pattern, a constant ratio hints at multiplicative.
9. PUZZLES (Arrangement, Ranking, Scheduling)
| Puzzle Type | Typical Clues | Solving Strategy |
|---|---|---|
| Ranking/Order | “A scored higher than B but lower than C”. | Create a inequality chain (A > B, C > A). Combine to get total order. |
| Scheduling (Time/Day) | “Meeting on Monday, not with X”. | Make a day‑slot matrix; fill fixed items, then use negatives. |
| Building/Floor | “Person on floor 3 lives above the one who likes tea”. | Assign floors, then cross‑reference attributes. |
| Lock‑Box/Key | “Key A opens box 2, not box 1”. | Use a bipartite matching approach. |
| Card/Token Distribution | “Each person gets 2 cards, one red, one black”. | Ensure each person satisfies constraints; use trial‑and‑error with back‑tracking. |
General Puzzle Solving Flow
- List all entities (persons, days, objects).
- Note down definite facts (e.g., “Person P is on floor 2”).
- Convert relative clues into inequalities or positional statements. 4. Create a grid/table (entities vs. attributes).
- Fill in certainties first, then use process of elimination for ambiguities.
- Iterate – each new placement may unlock further clues.
- Check for consistency after each fill; backtrack if contradiction appears.
Mnemonic: Definite Inequalities Grid Eliminate Iterate → “D I G E I” (pronounce “dig‑ei”). Reminds you to start with definite facts, then use inequalities, grid, elimination, and iterate.
10. DATA SUFFICIENCY
| Step | Action |
|---|---|
| 1. Understand the question | Identify what exactly is being asked (value, yes/no, relationship). |
| 2. Evaluate Statement 1 alone | Does it give enough info to answer? If yes → Answer A (1 sufficient). |
| 3. Evaluate Statement 2 alone | Same as above → Answer B (2 sufficient). |
| 4. Evaluate Both together | If neither alone works but combined they do → Answer C (both needed). |
| 5. If still insufficient → Answer D (data insufficient). | |
| 6. Never assume – only use what is explicitly given. |
Quick Checks
- For numeric value: Look for equations that can isolate the unknown. – For yes/no: See if the statement forces a definitive truth value.
- For ordering/ranking: Check if a clear relative position can be deduced.
Mnemonic: Status Of Unknown Needed → “S O U N” (think of “SOUND”). If the statement makes the unknown sound clear → sufficient.
11. VENN DIAGRAMS (Logical)
| Region | Meaning |
|---|---|
| Only A | Elements in A but not in B or C. |
| Only B | … |
| Only C | … |
| A ∩ B only | In both A and B, but not C. |
| B ∩ C only | … |
| A ∩ C only | … |
| A ∩ B ∩ C | In all three. |
| Outside all | In universal set but none of A, B, C. |
Solving Tips – Draw three overlapping circles labelled A, B, C.
- Start filling from the innermost region (triple overlap) if data given.
- Proceed to pairwise regions, then to singletons.
- Use subtraction: If total in A is known and you have filled A∩B and A∩C, then “Only A” = Total A – (A∩B) – (A∩C) + (A∩B∩C) (add back triple because subtracted twice).
- Check consistency: Sum of all regions must equal the universal total (if given).
Mnemonic: Inner Pair Single Outside → “I P S O” (think of “IPSO” – a legal term). Reminds you the order of filling.
12. STATEMENT‑ASSUMPTION / STATEMENT‑CONCLUSION
| Type | What to Test |
|---|---|
| Assumption | Is the statement implicitly required for the argument to hold? If negating it makes the argument fall → it’s an assumption. |
| Conclusion | Does the statement logically follow from the given premises? If yes → valid conclusion; if not → invalid. |
Quick Tests
- Assumption Negation Test: Assume the opposite of the candidate assumption. If the original statement becomes doubtful or false → the assumption is necessary.
- Conclusion Entailment Test: Try to derive the conclusion using only the premises (apply syllogism, conversion, etc.). If you can, it’s valid.
Mnemonic: Assume Negate Check → “A N C” (think of “ANC” – a political party, easy to recall). For conclusions: Entail Verify Conclusion → “E V C” (think of “EVC” – a video format).
13. CRITICAL REASONING (Argument‑Based)
| Element | Description |
|---|---|
| Premise | Fact or evidence supporting the argument. |
| Conclusion | Claim the arguer wants you to accept. |
| Assumption | Unstated bridge needed for premise → conclusion. |
| Strengthener | Information that makes the conclusion more likely. |
| Weakener | Information that undermines the conclusion. |
| Analogy | Comparison to a similar situation to support/refute. |
Approach
- Identify conclusion (often signalled by “therefore”, “thus”, “hence”).
- List premises (signal words: “because”, “since”, “as”).
- Spot the gap – what must be true for premises to lead to conclusion? That’s the assumption.
- Evaluate answer choices:
- Strengthener adds support to the assumption or directly to the conclusion.
- Weakener attacks the assumption or provides a counter‑example.
- Irrelevant does not affect the link.
Mnemonic: Conclusion Premise Assumption Strengthen Weakener → “C P A S W” (think of “CPA SW” – a certified public accountant who sweeps weak arguments).
14. QUICK REFERENCE TABLES
14.1 Logical Connectives (for statement‑based questions)
| Symbol | Meaning | Truth Table (p, q) |
|---|---|---|
| ∧ (AND) | True only if both true | T T → T; otherwise F |
| ∨ (OR) | True if at least one true | F F → F; otherwise T |
| → (IMPLIES) | False only when p true & q false | T T → T; T F → F; F T → T; F F → T |
| ↔ (IFF) | True when both same | T T → T; T F → F; F T → F; F F → T |
| ¬ (NOT) | Inverts truth | T → F; F → T |
14.2 Number Series Patterns (common in JKSSB)
| Pattern | Example | How to Spot |
|---|---|---|
| Add constant | 2, 5, 8, 11… (+3) | Difference same each step. |
| Multiply constant | 3, 6, 12, 24… (×2) | Ratio same each step. |
| Add increasing | 1, 2, 4, 7, 11… (+1,+2,+3,+4) | Differences themselves increase by 1. |
| Square / Cube | 1, 4, 9, 16… (n²) | Terms are perfect squares/cubes. |
| Alternating | 5, 9, 5, 9… | Two‑term repeat. |
| Prime | 2, 3, 5, 7, 11… | Only primes. |
| Mixed | 2, 6, 12, 20… (n×(n+1)) | Look for n·(n+1) pattern. |
Tip: Write down the first‑order differences; if they form a recognizable pattern (constant, AP, GP), you’ve found the rule.
14.3 Direction‑Turn Cheat Sheet
| From | Turn Left | Turn Right | U‑Turn |
|---|---|---|---|
| N | W | E | S |
| E | N | S | W |
| S | E | W | N |
| W | S | N | E |
| NE | NW | SE | SW |
| NW | SW | NE | SE |
| SE | SW | NE | NW |
| SW | SE | NW | NE |
15. FINAL REVISION CHECKLIST (Before the Exam)
- [ ] Spend ≤2 min on each question; if stuck, mark and move on. – [ ] Draw a quick diagram for seating, blood relation, direction, Venn, puzzles.
- [ ] Check for hidden negatives (“not”, “none”, “never”) – they often flip the answer.
- [ ] Verify units (metres vs. kilometres, hours vs. minutes) in direction/speed questions.
- [ ] Eliminate obviously wrong options first – improves odds if you must guess.
- [ ] Keep calm – anxiety leads to misreading left/right or mixing up premise/conclusion.
- [ ] If time permits, re‑read the question stem to ensure you answered what was asked (value, direction, relation, true/false). —
16. MEMORY AIDS (One‑Liners)
- Syllogism Mood – All Elephants In Orange Jelly → A‑E‑I‑O.
- Figure Order – 1st, 2nd, 3rd, 4th → think of a staircase climbing (1→2→3→4).
- Blood Relations – Father Mother Son Daughter Brother Sister Husband Wife → “FMSDB SHW”.
- Directions – Never Eat Soggy Waffles → N‑E‑S‑W (clockwise).
- Coding – Shift Opposite Reverse Jumble Matrix → “S O R J M”.
- Data Sufficiency – Status Of Unknown Needed → “S O U N”. – Assumption – Assume Negate Check → “A N C”.
- Conclusion – Entail Verify Conclusion → “E V C”.
- Venn – Inner Pair Single Outside → “I P S O”.
- Puzzle – Definite Inequalities Grid Eliminate Iterate → “D I G E I”. – Critical Reasoning – Conclusion Premise Assumption Strengthen Weakener → “C P A S W”.
End of Notes – Review these points, practice a few mixed sets, and you’ll be ready to tackle Section D of the JKSSB Forester Exam with confidence. Good luck!
