Logical Reasoning
Section A · Futures First International — Market Trading Intern OA
📌 What Has Been Asked (OA & Rounds)
| Format | Typical Question Style |
|---|---|
| OA (MCQ) | "What comes next: 2, 6, 12, 20, 30, ?" (Number series) |
| OA | "If COMPUTER is coded as RFUVQNPC, how is LAPTOP coded?" (Coding-Decoding) |
| OA | "A says to B: 'You are my mother's husband's sister's son.' How is B related to A?" (Blood Relations) |
| OA | "A person walks 5 km North, then 3 km East, then 5 km South. How far from start?" (Direction) |
| OA | "Find the odd one out: 3, 5, 11, 14, 17, 21" |
| Buzzer | Quick pattern recognition — "Next in: 1, 1, 2, 3, 5, 8, ?" → 13 |
| Attention test | "How many triangles in this figure?" |
Logical reasoning in FF tests speed of pattern recognition, not deep logical thinking. You should solve these in 15-20 seconds each.
PART 1: NUMBER SERIES
🧠 Common Patterns
| Pattern | Example | Rule |
|---|---|---|
| Constant difference | 3, 7, 11, 15, 19 | +4 |
| Increasing difference | 2, 5, 10, 17, 26 | +3, +5, +7, +9 (odd numbers) |
| Squares | 1, 4, 9, 16, 25 | n² |
| Cubes | 1, 8, 27, 64, 125 | n³ |
| n² + 1 | 2, 5, 10, 17, 26 | n² + 1 |
| n² − 1 | 0, 3, 8, 15, 24 | n² − 1 |
| Triangular | 1, 3, 6, 10, 15 | +2, +3, +4, +5 |
| Geometric | 3, 6, 12, 24, 48 | ×2 |
| Mixed | 2, 6, 12, 20, 30 | +4, +6, +8, +10 (or n(n+1)) |
| Fibonacci-like | 1, 1, 2, 3, 5, 8 | each = sum of prev two |
| Alternating | 2, 5, 3, 7, 4, 9 | two interleaved series: 2,3,4 and 5,7,9 |
| Prime numbers | 2, 3, 5, 7, 11, 13 | consecutive primes |
| Factorial | 1, 2, 6, 24, 120 | n! |
⚡ Speed Method
- First check: Is the difference constant? → arithmetic progression
- Then check: Is the ratio constant? → geometric progression
- Then check: Are the differences forming a pattern? → second-order differences
- Then check: Do terms match n², n³, n!, primes, or n(n+1)?
- Last resort: Are two series interleaved? (check alternate terms separately)
PART 2: CODING-DECODING
🧠 Common Coding Types
Type 1: Letter Shifting
Each letter shifted by a fixed number.
+1 shift: A→B, B→C, ... Z→A
+2 shift: A→C, B→D, ...
−1 shift: B→A, C→B, ...Example: If CAT = DBU (+1 shift), then DOG = EPH
Type 2: Reverse Alphabet
A=26, B=25, ... Z=1 (or A↔Z, B↔Y, C↔X...)
Position mapping: A(1)↔Z(26), B(2)↔Y(25), C(3)↔X(24), ...Formula: New position = 27 − Old position
Type 3: Position-Based Coding
Letters replaced by their position numbers (A=1, B=2, ... Z=26)
Type 4: Word-Level Rearrangement
Letters within the word are rearranged (reversed, swapped in pairs, etc.)
COMPUTER → RETUPMOC (reversed)
COMPUTER → OCMPUTRE (pairs swapped)Type 5: Number-Based Coding
If TABLE = 56, CHAIR = ? → Sum of positions: T(20)+A(1)+B(2)+L(12)+E(5) = 40... check pattern.
⚡ Speed Method
- Write down the position of each letter in both original and coded words
- Find the shift/pattern between positions
- Apply the same pattern to the question word
PART 3: BLOOD RELATIONS
🧠 Key Relationships Map
Grandfather ─── Grandmother
│
┌──────────┴──────────┐
Father/Uncle Mother/Aunt
│ │
┌──────┴──────┐ ┌──────┴──────┐
Son Daughter Son Daughter
(Brother) (Sister) (Cousin) (Cousin)Key Relationships Quick Reference
| Statement | Relation |
|---|---|
| "A's father's son" | A's brother (or A himself) |
| "A's mother's daughter" | A's sister (or A herself) |
| "A's father's father" | A's grandfather |
| "A's mother's husband" | A's father |
| "A's father's wife" | A's mother |
| "A's brother's wife" | A's sister-in-law |
| "A's mother's brother" | A's maternal uncle |
| "A's father's sister" | A's aunt (bua/phuphi) |
| "A's mother's mother's husband" | A's maternal grandfather |
⚡ Speed Method: ALWAYS Draw a Family Tree
- Use → for "parent of", = for "married to"
- Male (M), Female (F) — label immediately
- Work from inside out (simplify inner relationship first)
Example: "A's mother's husband's sister's son"
- A's mother's husband = A's father
- A's father's sister = A's aunt
- A's aunt's son = A's cousin
Common Coded Blood Relations
A + B → A is father of B
A − B → A is mother of B
A × B → A is brother of B
A ÷ B → A is sister of BBuild the tree from the coding, then answer.
PART 4: DIRECTION & DISTANCE
🧠 Framework
North
|
West ─────┼───── East
|
SouthKey Patterns
- Right turn from North = East, Right from East = South, etc.
- Left turn from North = West, Left from West = South, etc.
- After a sequence of walks, use Pythagoras for straight-line distance
Example: Walk 5 km North, 3 km East, 5 km South.
- North and South cancel: net North = 0
- Net East = 3 km
- Distance from start = 3 km (due East)
Trick: Track Net Displacement
Keep a running tally of (North-South, East-West):
Start: (0, 0)
5 km N: (5, 0)
3 km E: (5, 3)
5 km S: (0, 3)
Distance = √(0² + 3²) = 3 kmPART 5: ODD ONE OUT / CLASSIFICATION
Common Bases for Grouping
- Primes vs composites: 2, 3, 5, 7, 9, 11 → 9 is odd one out (not prime)
- Squares vs non-squares: 4, 9, 16, 18, 25 → 18 is out
- Even vs odd
- Alphabetical pattern
- Semantic grouping: Apple, Mango, Potato, Banana → Potato (not a fruit)
📝 Practice Questions (with Answers)
Q1. What comes next: 2, 3, 5, 8, 13, 21, ?
A: Differences: 1, 2, 3, 5, 8 — these are the Fibonacci sequence! Next diff = 13. Answer = 21 + 13 = 34 Alternatively: this IS the Fibonacci sequence starting from 2,3. Next = 34.
Q2. If in a code, MANGO is written as OCPIQ, how is APPLE written?
A: M+2=O, A+2=C, N+2=P, G+2=I, O+2=Q. Pattern: +2 shift. A+2=C, P+2=R, P+2=R, L+2=N, E+2=G. Answer: CRRNG
Q3. A is B's sister. C is B's mother. D is C's father. E is D's mother. How is A related to D?
A: D is C's father. C is A's mother. So D is A's maternal grandfather → A is D's granddaughter.
Q4. Find the odd one out: 121, 144, 169, 196, (225), (256). Wait — Find odd: 8, 27, 64, 100, 125, 216
A: These are cubes: 2³=8, 3³=27, 4³=64, 5³=125, 6³=216. 100 is the odd one (not a cube; 100 = 10²).
Q5. Next in series: 1, 4, 9, 16, 25, 36, ?
A: Perfect squares: 1², 2², 3², ... 7² = 49
Q6. A man walks 4 km East, 3 km North, 4 km West. How far is he from start and in which direction?
A: East-West cancel. Net = 3 km North. Distance = 3 km.
Q7. If ROSE is coded as 6821, CHAIR is coded as 73456, and PREACH is coded as 961473, what is the code for SEARCH?
A: S=2, E=1, A=4, R=6, C=7, H=3. SEARCH = 214673
🔑 Exam Strategy
- Series: Spend max 15 seconds. If the pattern isn't obvious by then, skip — these are traps for time
- Coding-Decoding: Write out positions immediately. Don't try to do it in your head
- Blood Relations: ALWAYS draw a tree. Mental solving leads to errors under pressure
- Direction: Track (North, East) coordinates — Pythagoras at the end
- Odd one out: Check primes, squares, cubes first — covers 80% of questions
- These are the highest skip-rate questions for many candidates — if you can nail them quickly, you get a massive edge
- FF's attention-to-detail rounds overlap with LR — practice "how many triangles in this figure" type questions separately