Number & Letter Series
Types of Series Patterns
| Pattern Type | Example | Logic |
|---|---|---|
| Arithmetic | 2, 5, 8, 11, ? | +3 each time → 14 |
| Geometric | 3, 6, 12, 24, ? | ×2 each time → 48 |
| Squares | 1, 4, 9, 16, 25, ? | 1², 2², 3²... → 36 |
| Cubes | 1, 8, 27, 64, ? | 1³, 2³, 3³... → 125 |
| Fibonacci-type | 2, 3, 5, 8, 13, ? | Each = sum of previous two → 21 |
| Difference pattern | 1, 2, 4, 7, 11, ? | Diff: +1,+2,+3,+4... → 16 |
| Prime numbers | 2, 3, 5, 7, 11, 13, ? | Next prime → 17 |
| Mixed operation | 5, 12, 26, 54, ? | ×2+2 → 110 |
Letter Series Approach
Alphabet positions: A=1, B=2 ... Z=26. EJOTY trick: E=5, J=10, O=15, T=20, Y=25. Memorise these 5 → derive all others.
A↔Z, B↔Y, C↔X ... (sum = 27). If A=1, opposite = 27−1 = 26 = Z. Quick: A-Z, B-Y, C-X, D-W, E-V, F-U, G-T, H-S, I-R, J-Q, K-P, L-O, M-N
D(4) → G(7): +3
G(7) → K(11): +4
K(11) → P(16): +5
P(16) → ?(16+6=22): V
Find the missing term: 3, 7, 15, 31, 63, ?CGL-level difficulty
Find odd one out: 8, 27, 64, 100, 125Number property
Analogy
Types of Analogies
| Relationship Type | Example |
|---|---|
| Tool : User | Scalpel : Surgeon :: Chisel : Carpenter |
| Young one | Cat : Kitten :: Horse : Foal |
| Habitat | Lion : Den :: Bee : Hive |
| Product : Material | Shoe : Leather :: Paper : Wood |
| Worker : Workplace | Teacher : School :: Doctor : Hospital |
| Part : Whole | Leaf : Tree :: Chapter : Book |
| Cause : Effect | Fire : Ash :: Flood : Damage |
| Antonym pair | Hot : Cold :: Fast : Slow |
| Number pattern | 6 : 36 :: 8 : 64 (n : n²) |
BDFH: B(2), D(4), F(6), H(8) — even positions (each +1)
PRTV: P(16), R(18), T(20), V(22)
Each +1: Q(17), S(19), U(21), W(23) = QSUW
Coding-Decoding
Types of Coding
Letter Shift Coding
Pattern: each letter +2
D(4)+2=F(6), O(15)+2=Q(17), G(7)+2=I(9) = FQI
Reverse Coding
A↔Z, B↔Y ... (use the opposite letter rule). If DOOR is coded as WLLC → each letter replaced by its opposite.
D(4)→W(23), O(15)→L(12), O(15)→L(12), R(18)→I(9) ✓
Number for Letter Coding
P=1, E=6, L=3, I=4, C=5, A=?, N=?
A and N have no code assigned. Only known letters: 163451 _ _
(In CGL, such questions usually have all letters from original word — check options!)
Word-coded Conditions
When symbols replace operations or words replace numbers — always establish the pattern from the given example, then apply consistently. Never assume; always derive from the example.
Blood Relations
Family Tree Symbols
Always draw a family tree. Use □ for male, ○ for female, = for married couple, | or / for parent-child, — for siblings.
Key Relations
| Relation | Meaning |
|---|---|
| Uncle | Father's/Mother's brother OR father's/mother's sister's husband |
| Aunt | Father's/Mother's sister OR father's/mother's brother's wife |
| Nephew | Brother's/Sister's son |
| Niece | Brother's/Sister's daughter |
| Maternal uncle | Mother's brother (Mama) |
| Paternal uncle | Father's brother (Chacha/Tau) |
| Cousin | Uncle's or aunt's child |
C (female) = B's mother → C is also A's mother
D = C's father → D is A's grandfather (maternal)
Answer: A is D's granddaughter
Pointing to a man in a photograph, a woman says "His mother's only daughter is my mother." How is the woman related to the man?Classic CGL question
Syllogism
Venn Diagram Method
Always draw Venn diagrams. Never assume anything beyond what the statements say. "Some" means at least one; "All" means 100%; "No" means zero overlap.
Standard Conclusions Table
| Statement 1 | Statement 2 | Definite 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 ✓ |
| Some A are B | No B is C | Some A are not C ✓ |
| All A are B | Some B are C | No definite conclusion about A and C |
| Some A are B | Some B are C | No definite conclusion |
Statement 2: Some dogs are also in "rats" circle
Can we guarantee cats are in the "some dogs that are rats" part? NO — the "some dogs = rats" may be entirely outside the "cats" group.
Conclusion I: Does NOT follow
Conclusion II: Does NOT follow
When neither conclusion I nor II alone follows, but they are complementary (one positive, one negative about same pair), check if "Either I or II follows" applies. This happens when statements give no definite answer and conclusions exhaust all possibilities.
Direction Sense
Direction Framework
North is UP, South is DOWN, East is RIGHT, West is LEFT. Always draw on paper as you read each step. Final answer = straight-line distance (use Pythagoras if needed).
Turns
Clockwise (Right Turn)
- N → E → S → W → N
- Facing North, turn right → face East
Anti-clockwise (Left Turn)
- N → W → S → E → N
- Facing North, turn left → face West
Net East-West: 6−4 = 2m East
Distance = √(7² + 2²) = √(49+4) = √53 ≈ 7.28m
(In MCQ context, √53 or exact radical will be the option)
Ranking & Order
Key Formulas
Total = Rank from top + Rank from bottom − 1
Rank from bottom = Total − Rank from top + 1
If A and B interchange, A now has B's original rank. No change in total count. Just read who's at what position carefully.
Matrix & Figure Questions
Approach
- Figure Matrix: Find the relationship between figures in each row (or column). Apply the same rule to find the missing figure.
- Number Matrix: Check row totals, column totals, diagonal patterns, or operation between cells.
- Check both rows AND columns before deciding the rule.
Row 2: 3 × 6 = 18 ✓
Rule: col1 × col2 = col3
Row 3: 5 × 7 = 35
Venn Diagrams
Types of Questions
Type 1 — Which diagram represents the relation?
Identify if groups have: complete overlap (A inside B), partial overlap (intersecting circles), or no overlap (separate circles).
- Doctors : Humans : Animals → Humans completely inside Animals, Doctors partially overlap Humans
- Men : Women : Humans → Men and Women separately inside Humans, no overlap with each other
Type 2 — Data from Venn diagram
Only A = A − (A∩B) − (A∩C) + (A∩B∩C)
Only A and B (not C) = (A∩B) − (A∩B∩C)
At least one = A + B + C − (A∩B) − (B∩C) − (A∩C) + (A∩B∩C)
Mirror & Water Image
Rules
Mirror Image (Vertical mirror)
- Left ↔ Right flipped
- Up/Down remains same
- Clock: 3 o'clock position becomes 9 o'clock
- Letters: A, H, I, M, O, T, U, V, W, X, Y are symmetric (same as mirror)
Water Image (Horizontal mirror)
- Up ↔ Down flipped
- Left/Right remains same
- Clock: 12 o'clock becomes 6 o'clock
- Think of reflection in water — only top/bottom flips
Mirror image time = 11:60 − actual time (if time has minutes) OR 12:00 − actual time (if no minutes).
Example: Mirror of 4:20 = 11:60 − 4:20 = 7:40