🧠 Reasoning — Master Notes

Verbal, Non-Verbal & Analytical Reasoning | RRB NTPC CBT-1 & CBT-2

📚 5000+ Words ⚡ All Topics Covered 🌟 PYQ Patterns 📌 30–35 Questions in Exam

🔢 1. Number Series

Number series is the most-asked topic in reasoning. You must find the pattern and identify the missing/wrong term.

Types of Number Series Patterns

Pattern Type	Example	Logic
Arithmetic (AP)	3, 7, 11, 15, ?	+4 each time → 19
Geometric (GP)	2, 6, 18, 54, ?	×3 each time → 162
Squares	1, 4, 9, 16, 25, ?	1², 2², 3²... → 36
Cubes	1, 8, 27, 64, ?	1³, 2³, 3³... → 125
Difference of differences	2, 3, 6, 11, 18, ?	Diff: 1,3,5,7 (odd) → 27
Alternate terms	1, 2, 4, 5, 7, 8, ?	Two APs merged → 10
Fibonacci-type	1, 1, 2, 3, 5, 8, ?	Each = sum of prev two → 13
×n ± k	1, 3, 7, 15, 31, ?	×2+1 each time → 63
Prime numbers	2, 3, 5, 7, 11, ?	Consecutive primes → 13

Step-by-Step Approach to Any Series

1 Calculate differences between consecutive terms

2 If differences form a pattern — it's an AP-based series

3 Calculate ratios — if constant, it's a GP-based series

4 Check if terms are squares, cubes, or primes

5 If none above — try alternate terms or combination patterns

PYQ Example: 4, 9, 25, 49, 121, ?
Pattern: 2², 3², 5², 7², 11² → these are squares of prime numbers
Next prime = 13, so answer = 13² = 169

💡 Speed Tricks

Always check: is there a pattern with +1, +2, +3 differences first?
Check if all terms are multiples of some number
Wrong number in series: substitute options to check which breaks the pattern

🔤 2. Alphabet Series & Coding

Alphabet Position Values (Essential Memory)

Letter	Position	Letter	Position	Reverse Position (27-n)
A	1	N	14	A=26, B=25, C=24...
E	5	P	16	Z=1, Y=2, X=3...
I	9	S	19	N=13 (middle)
J	10	T	20	M=14, N=13
M	13	Z	26

🧠 Memory Trick — EJOTY: E=5, J=10, O=15, T=20, Y=25 → every 5th letter

Alphabet Series Patterns

Skipping Pattern

A, C, E, G, ? → +2 (skip 1) → I
B, E, H, K, ? → +3 (skip 2) → N
A, D, H, M, ? → +3,+4,+5,+6 → S

Reverse Pattern

Z, Y, X, W, ? → −1 → V
Z, X, V, T, ? → −2 → R
ZA, YB, XC, ? → WD

Coding-Decoding — All Types

Type 1: Letter Substitution

Common Coding Patterns

Each letter replaced by next: A→B, B→C... (shift +1)
Each letter replaced by previous: B→A, C→B... (shift −1)
Letters coded by their position numbers: A=1, B=2...
Reversed alphabet: A→Z, B→Y, C→X... (26+1-n)
Skip pattern: DOOR → FQQT (each +2)

Type 2: Word Substitution (Swapping)

Example: If "ROME" is coded as "OMRE", then "HELP" = ?
Pattern: Letters 1&2 swap, letters 3&4 swap → H-E-L-P → EHLP → EHLP

Type 3: Number-based Coding

Decode the Rule

If CAT = 48 → C(3)+A(1)+T(20)=24; 24×2=48 (sum × 2)
If DOOR = 41 → D(4)+O(15)+O(15)+R(18)=52; 52-11=41... check the pattern
Always find the rule from two examples given, then apply to third

Type 4: Direction-based Coding

Example: In a code: North↔South, East↔West
"Walk North then East" → coded as "Walk South then West"

💡 Tricks for Coding-Decoding

First identify the number of letters — same in code & original?
Find the shift value from one known letter pair
Check if letters are reversed within the word
For number coding: always find sum/product/position pattern from examples

🔗 3. Analogies

An analogy asks: "A is to B as C is to ?". You must find the relationship between the first pair, then apply it.

Relationship Types in Analogies

Relationship	Example	Answer
Tool : Worker	Pen : Writer	Brush : Painter
Animal : Sound	Dog : Bark	Cat : Meow
Animal : Young	Cow : Calf	Horse : Foal
Animal : Dwelling	Dog : Kennel	Horse : Stable
Part : Whole	Petal : Flower	Chapter : Book
Product : Raw Material	Bread : Wheat	Sugar : Sugarcane
Word : Synonym	Happy : Joyful	Sad : Sorrowful
Cause : Effect	Fire : Smoke	Exercise : Fatigue
Study of : Field	Ornithology : Birds	Seismology : Earthquakes
Instrument : Measurement	Thermometer : Temperature	Barometer : Pressure

Key Scientific Analogies (PYQ Favourites)

Ophthalmology : Eyes :: Cardiology : Heart
Stethoscope : Doctor :: Sextant : Navigator
Seismology : Earthquake :: Meteorology : Weather
Entomology : Insects :: Herpetology : Reptiles
Currency : India = Rupee :: Japan = Yen

💡 Strategy for Analogies

State the relationship in a sentence: "A is a type of B", "A produces B", "A is used by B"
Apply exactly the same relationship to find the answer
Be careful of direction: Pen:Writer ≠ Writer:Pen
If multiple options seem valid — pick the most specific/direct relationship

📃 4. Classification (Odd One Out)

Find the item that does NOT belong to the same category as the others.

Common Classification Types

Category-based

Dog, Cat, Sparrow, Cow → Sparrow (bird; others = mammals)
Mars, Earth, Venus, Moon → Moon (natural satellite; others = planets)
Gold, Silver, Steel, Platinum → Steel (alloy; others = pure metals)

Number-based (Odd One Out)

16, 36, 56, 64, 100 → 56 (others are perfect squares)
8, 27, 64, 100, 125 → 100 (others are perfect cubes)
3, 5, 7, 9, 11 → 9 (others are primes; 9 = 3²)

PYQ: Wheat, Rice, Mango, Barley → Mango (fruit; others are cereals/grains)

📌 Exam Alert: Sometimes two items could be odd — pick the one that is most clearly different and where the other three form the most specific/consistent group.

👪 5. Blood Relations

Family Relationship Chart

Term	Meaning
Parent's parent	Grandparent (Grandfather/Grandmother)
Parent's sibling	Uncle (Mama/Chacha/Fufa) or Aunt (Mausi/Chachi/Bua)
Sibling's child	Nephew (son) or Niece (daughter)
Parent's sibling's child	Cousin
Spouse's parent	Father-in-law / Mother-in-law
Spouse's sibling	Brother-in-law / Sister-in-law
Sibling's spouse	Brother-in-law / Sister-in-law

Solving Blood Relation Problems — Method

1 Draw a family tree with boxes for each person

2 Use symbols: ▲ = Male, ● = Female, = = married couple, | = parent-child

3 Enter information from each sentence one by one

4 Identify the unknown relationship from the tree

PYQ: "Pointing to a man, a woman says, 'His mother is the only daughter of my mother.' How is the woman related to the man?"
"Only daughter of my mother" = woman herself
So: Woman's mother = man's mother → Woman is the man's Mother

Coded Blood Relations (Common Pattern)

A + B = A is parent of B
A − B = A is sibling of B
A × B = A is wife of B (or husband)
A ÷ B = A is son/daughter of B

💡 Common Traps

"Only son" doesn't mean no sisters — don't assume no siblings unless stated
Distinguish "X says to Y about Z" — who is saying, who is being described
In photo questions: "Looking at a photo, A says…" — A is the reference point

🌏 6. Direction Sense

Direction Chart

Compass Directions

N, NE, E, SE, S, SW, W, NW (clockwise)
Turning Right = Clockwise (North → East → South → West)
Turning Left = Anti-clockwise (North → West → South → East)
Opposite directions: N↔S, E↔W, NE↔SW, NW↔SE

Distance Calculation — Shortcut

For two perpendicular distances a and b: Direct distance = √(a² + b²) [Pythagoras Theorem] Common pairs: (3,4)→5 · (5,12)→13 · (8,15)→17 · (6,8)→10

PYQ: A walks 6 km North, then 8 km East. How far is he from the start?
Distance = √(6² + 8²) = √(36+64) = √100 = 10 km
Direction: North-East of starting point

Sun Direction Shortcuts

Shadow Rules

Morning (sunrise in East) → Shadows fall towards West
Evening (sunset in West) → Shadows fall towards East
Noon → Shadows fall towards North (in India/northern hemisphere)
If facing East in morning, shadow falls behind (West) → you face your shadow = facing West

💡 Tips for Direction Problems

Draw the path step by step on paper — never solve mentally
Always start from a fixed point and mark North upwards
"Towards the right side" means the right side of the face direction, not the page right
Final position question: use coordinates (x, y) and calculate Pythagoras

📚 7. Syllogism

Syllogism tests logical deduction from given statements. You must derive conclusions based ONLY on the statements provided.

Types of Statements

Statement Type	Format	Venn Diagram
Universal Positive (A)	All A are B	Circle A fully inside B
Universal Negative (E)	No A is B	Circles A and B completely separate
Particular Positive (I)	Some A are B	Circles A and B partially overlapping
Particular Negative (O)	Some A are not B	A partially outside B

Standard Conclusions Table

Statement 1	Statement 2	Conclusion
All A are B	All B are C	All A are C ✓
All A are B	No B is C	No A is C ✓
Some A are B	All B are C	Some A are C ✓
All A are B	Some B are C	Some A are C ✗ (cannot say)
No A is B	All B are C	Some C are not A ✓
Some A are B	No B is C	Some A are not C ✓

Complementary Pair Rule

Either...Or Conclusions

When neither "All A are B" nor "No A is B" can be definitively concluded — but exactly one must hold — they form a complementary pair
Complementary pairs: (All A is B) + (Some A is not B), or (Some A is B) + (No A is B)
If both conclusions individually fail but together they are complementary, mark "Either I or II follows"

PYQ:
Statements: All pens are books. Some books are copies.
Conclusions: I. Some pens are copies. II. Some copies are books.
Answer: Only conclusion II follows (Some copies are books = directly deducible from "Some books are copies" by conversion)

💡 Venn Diagram Method (Fastest)

Draw all possible Venn diagrams consistent with the statements
A conclusion is valid ONLY if it holds in ALL possible diagrams
Use 2-3 different arrangements to test each conclusion

🏛 8. Seating Arrangement

Types of Arrangements

Linear Arrangement

People sit in a row (one or two rows facing each other)
Left/Right is from the perspective of the person, not observer
If facing North: Right = East, Left = West
If facing South: Right = West, Left = East

Circular Arrangement

People sit around a table (round/hexagonal/square)
Facing the centre: Left = anti-clockwise, Right = clockwise
Facing outward: Left = clockwise, Right = anti-clockwise
Fix one person's position, arrange others relative to them

Step-by-Step Solving Method

1 List all people/objects to be arranged

2 Pick the most constrained person (most clues) — place them first

3 Fill in confirmed positions, then use elimination for remaining

4 Verify all conditions are satisfied at the end

📌 Important Rules for Circular:

"Immediate left" and "immediate right" = adjacent seats
"Opposite to" = directly across the table (for even-numbered seating, exactly n/2 positions away)
Draw the circle with all seats marked before placing people

★ 9. Mathematical Operations & Inequalities

Symbol Substitution

In these questions, standard operators (+, −, ×, ÷) are replaced by custom symbols. Decode and solve.

Example: If A means ×, B means ÷, C means +, D means −
Find: 20 A 5 C 10 D 3 B 3
= 20 × 5 + 10 − 3 ÷ 3
= 100 + 10 − 1 = 109

BODMAS Rule for Order of Operations

Brackets → Order (powers) → Division → Multiplication → Addition → Subtraction
Always apply BODMAS after substituting the real operators

Inequality-based Questions

Statement Inequality Rules

A > B > C → A > C (transitive) ✓
A > B > C → A > C ✓, but "A > C" is not necessarily valid if the chain breaks
A ≥ B ≥ C → A ≥ C ✓ (but not necessarily A > C)
When a chain has > and ≥ mixed: A > B ≥ C → A > C ✓
When chain has > and <: A > B < C → NO direct conclusion between A and C
Complementary pair for inequalities: "A > B" and "A ≤ B" form complementary pair

⏱ 10. Clock & Calendar

Clock Problems

Key Clock Facts

Clock = 360°; Hour hand covers 360° in 12 hrs → 0.5°/min
Minute hand covers 360° in 60 min → 6°/min
Relative speed of minute hand over hour hand = 6 − 0.5 = 5.5°/min
Minute & hour hands coincide every 720/11 minutes ≈ 65.45 minutes
Minute hand gains 55 minutes over hour hand in 60 clock minutes

Angle between hands at H hours M minutes: θ = |30H − 5.5M| degrees If θ > 180°: reflex angle = 360° − θ

PYQ: Find angle between clock hands at 3:25
θ = |30×3 − 5.5×25| = |90 − 137.5| = 47.5°

Calendar Problems

Year Type	Total Days	Odd Days
Ordinary year (365 days)	365	1 (365 = 52 weeks + 1 day)
Leap year (366 days)	366	2 (366 = 52 weeks + 2 days)
100 years	—	5 odd days
200 years	—	3 odd days
300 years	—	1 odd day
400 years	—	0 odd days

Leap Year Rules

Divisible by 4 → leap year (e.g., 2024)
Divisible by 100 → NOT a leap year (e.g., 1900)
Divisible by 400 → leap year (e.g., 2000)
2100, 2200, 2300 = NOT leap years; 2400 = leap year

💡 Day Calculation Shortcut

Code: Sun=0, Mon=1, Tue=2, Wed=3, Thu=4, Fri=5, Sat=6
If 1st Jan 2023 = Sunday, what day is 15th Jan 2023?
15th Jan = 1st Jan + 14 days = 14 odd days = 14 mod 7 = 0 → Sunday + 0 = Sunday

🍌 11. Ranking & Ordering

Total = Rank from Left + Rank from Right − 1 Position from Left = (Total + 1) − Position from Right

PYQ: In a class of 40 students, Ravi ranks 15th from the front. What is his rank from the back?
Rank from back = 40 + 1 − 15 = 26th

Ordering Problems (Height/Age/Weight)

Given Multiple Statements, Order All Items

Assign variables: A > B, C < D, B = D etc.
Build one consistent order from all inequalities
Be careful: "taller than" vs "shorter than" — draw a line with tallest on top

📄 12. Statement & Conclusion / Assumptions / Arguments

Key Distinctions

Type	Definition	Key Rule
Statement & Conclusion	Does the conclusion logically follow from the statement?	Must follow directly; no extra assumptions
Statement & Assumption	Is the assumption implicit (unstated but necessary)?	Must be necessary for statement to be true
Statement & Argument	Is the argument strong (relevant, practical) or weak?	Strong = directly relevant, practical, addresses main issue
Cause & Effect	Which statement is cause, which is effect?	Cause comes first; effect follows from it

PYQ — Statement & Assumption:
Statement: "Please don't go out in the sun without a hat."
Assumption I: "The sun can cause problems without a hat" — IMPLICIT ✓ (necessary for the advice)
Assumption II: "Wearing a hat in all weather is necessary" — NOT IMPLICIT ✗ (too broad)

💡 Strong vs Weak Arguments

Strong: Directly related to the question, practical, addresses the issue
Weak: Vague, emotional, irrelevant, extreme, hypothetical, or not addressing the real point
"People will misuse it" → usually weak (assumes the worst without evidence)

📸 13. Non-Verbal Reasoning (Figures & Patterns)

Mirror Image

Rules for Mirror Images

Mirror on the right/left side: image is HORIZONTAL flip (left↔right reversed)
Mirror on top/bottom: image is VERTICAL flip (up↔down reversed)
Letters that look the same in mirror: A, H, I, M, O, T, U, V, W, X, Y
Numbers unchanged in vertical mirror: 0, 1, 8
Clock mirror: if it shows 3:00, mirror shows 9:00 (use: 12:00 − shown time for left mirror = 12−3 = 9)

Water Image

Rules for Water Images

Water = horizontal mirror (top↔bottom reversed)
Left-right remains same; up-down is flipped
The base of the figure appears at the top in water image

Paper Folding & Cutting

Key Concept

When paper is folded and punched, unfold mentally in reverse order
Each fold doubles the pattern symmetrically
Fold line is axis of symmetry — holes appear in mirror positions across fold line

Figure Series / Embedded Figures

What to Look For

Count: sides, lines, shading, rotations
Each figure in a series changes one property at a time (rotation, shading, size)
For embedded figures: look for the target shape within the complex figure

📚 MASTER SUMMARY — REASONING QUICK REFERENCE

Topic	Avg. Questions (CBT-1)	Key Trick
Number Series	4–5	Check differences, ratios, squares, primes in order
Alphabet/Coding	3–4	EJOTY trick; identify shift value first
Analogies	2–3	State relationship as a sentence
Classification	2–3	Find the most specific common category for 3 items
Blood Relations	2–3	Draw family tree; identify gender from context
Direction Sense	2–3	Draw path; use Pythagoras for final distance
Syllogism	2–3	Venn diagram method; check all possible diagrams
Seating Arrangement	2–3	Fix most-constrained person first; draw circle/row
Mathematical Ops	1–2	Substitute symbols; apply BODMAS
Clock & Calendar	1–2	θ = \|30H−5.5M\|; Odd days method
Ranking/Order	1–2	Total = Rank from front + Rank from back − 1
Non-Verbal	2–3	Mirror: flip L↔R; Water: flip U↔D

✅ Exam Strategy for Reasoning

In 90 minutes (CBT-1), you have ~90 seconds per question — reasoning is fastest to score
Attempt Number Series, Analogies, Classification, Alphabet Coding first (fastest)
Blood Relations and Seating Arrangement take more time — attempt after easier ones
For syllogism: always draw at least 2 Venn diagrams per question
Never attempt reasoning mentally — always draw/write on rough paper