Logical Reasoning: Series, Coding & Puzzles

Reasoning questions look like puzzles but are really pattern-spotting: the same seven or eight patterns appear again and again — number series, letter series, coding-decoding, blood relations, directions, odd-one-out and clock angles. Learn to recognise the pattern, and the answer falls out in seconds.

Number & Letter Series

For a number series, first check the differences between terms. Example: 2, 6, 12, 20, 30, ? — differences are 4, 6, 8, 10 (increasing by 2), so the next difference is 12 → answer 42. (Bonus pattern: these are 1×2, 2×3, 3×4, 4×5, 5×6, so next is 6×7 = 42.)

For a letter series, convert letters to positions (A=1 … Z=26). Example: A, C, F, J, O, ? — positions 1, 3, 6, 10, 15 with gaps +2, +3, +4, +5 → next gap +6 → position 21 = U.

🧠 Memory trick

Write A=1 … Z=26 at the top of your rough sheet the moment the exam starts. Half of all coding and series questions become mechanical once the number line is in front of you. Also memorise the reverse pairs: A↔Z, B↔Y, C↔X (positions adding to 27).

Coding–Decoding & Odd One Out

Shift codes: if MOBILE is written as NPCJMF, every letter moved +1 (M→N, O→P…). Apply the same shift to the new word: PHONE → QIPOF.
Value codes: if CAT = 24, check letter positions: C(3) + A(1) + T(20) = 24 — it is a sum code. Then DOG = 4 + 15 + 7 = 26.
Odd one out: look for the property shared by all but one. In 3, 5, 7, 9, 11 every number is prime except 9 (9 = 3 × 3).

Analogy — Word & Number Pairs

Analogy questions ask A : B :: C : ? — find the exact relationship between A and B, then apply the same relationship to C. The relationship can be a meaning link (words) or a mathematical link (numbers).

Common types of word analogy
Relationship type	Example
Worker : Tool/Place	Doctor : Stethoscope :: Carpenter : Saw
Part : Whole	Page : Book :: Petal : Flower
Synonym	Big : Large :: Small : Tiny
Antonym	Hot : Cold :: Day : Night
Young–Adult (animal names)	Puppy : Dog :: Calf : Cow

Number analogy works the same way but with an arithmetic rule. Example: 4 : 16 :: 5 : ? — the rule is "square the number" (4² = 16), so 5² = 25. Example 2: 3 : 27 :: 4 : ? — the rule is "cube the number" (3³ = 27), so 4³ = 64.

⚠️ Exam trap

Always verify your rule works both ways in the options before finalising — a common trap is finding a relationship (e.g. "both are animals") that is too vague, when the intended relationship is more specific (e.g. "young–adult pair of the same species"). Check that only one option fits the precise rule.

Blood Relations, Directions & Clocks

Blood relations: decode phrase by phrase from the inside out. "She is the daughter of my grandfather's only son" → grandfather's only son = my father → his daughter = my sister.
Directions: always sketch. Facing north, a right turn faces you east; a left turn faces you west. Distances at right angles combine by Pythagoras: 3 km north then 4 km east = 5 km from the start (3-4-5 triangle).
Clocks: the hour hand moves 30° per hour, the minute hand 6° per minute. At 3:00 the angle between the hands is 3 × 30° = 90°.

💡 Think of it like this

Treat every reasoning question like detective work with a pencil: draw the family tree, draw the walking path, write the letter numbers. Aspirants who solve "in the head" make careless slips; the pencil never does.

A distinct, frequently-tested variant of blood relations uses symbols in place of relation words — you must first decode which symbol means which relationship, then trace a chain.

Typical key: "P + Q" means P is the mother of Q; "P − Q" means P is the brother of Q; "P × Q" means P is the father of Q; "P ÷ Q" means P is the sister of Q.
Worked example: "A + B × C − D" means: A is mother of B; B is father of C; C is brother of D. So A is B's mother, B is C's father → A is C's grandmother; and since C is D's brother, D is also A's grandchild — specifically, A is D's grandmother too (through the same chain, assuming D is C's sibling).

🧠 Memory trick

Decode the symbols first, in isolation, before touching the actual chain — write "+ = mother, − = brother, × = father, ÷ = sister" on your rough sheet, then substitute. Solving symbol and relation simultaneously is where most mistakes happen.

Key takeaways

Number series: check differences first (2, 6, 12, 20, 30 → +4, +6, +8, +10 → next 42).
Letter puzzles: write A=1 … Z=26 immediately; reverse pairs add to 27 (A↔Z, B↔Y).
Coding: test a constant shift (+1, −1…) or a sum of positions; apply the same rule to the asked word.
Blood relations: decode inside-out ("grandfather's only son" = father). Directions: sketch; right-angle legs combine by Pythagoras (3-4-5).
Clocks: hour hand 30°/hour, minute hand 6°/minute; at 3:00 the angle is 90°.
Always solve on paper — draw the tree, the path, the number line. The pencil beats the head.
Analogy = A : B :: C : ? — find the exact relationship (worker-tool, part-whole, synonym/antonym, young-adult, or a math rule like squaring/cubing) and verify it fits precisely before answering.
Coded blood relations use symbols (e.g. + = mother, − = brother, × = father, ÷ = sister) — decode the symbol key first, then trace the chain left to right.

Practice questions (11)

Attempt each one before opening the answer. Every explanation names the tempting wrong option as well as the right one, because that is where marks are lost.

Find the next term: 2, 6, 12, 20, 30, ?
1. 36
2. 40
3. 42
4. 44
Show answer
Answer: C — 42
Differences are 4, 6, 8, 10 → next difference 12 → 30 + 12 = 42. (Pattern n(n+1): 6×7 = 42.)
In a code, CAT = 24 (sum of letter positions). What is DOG?
1. 25
2. 26
3. 27
4. 28
Show answer
Answer: B — 26
The code is the sum of alphabet positions, confirmed by CAT = 3 + 1 + 20 = 24. So DOG = D(4) + O(15) + G(7) = 26. The EJOTY anchors (E=5, J=10, O=15, T=20, Y=25) let you place O at 15 without counting from A.
Find the next letter: A, C, F, J, O, ?
1. S
2. T
3. U
4. V
Show answer
Answer: C — U
Positions 1, 3, 6, 10, 15 with gaps +2, +3, +4, +5 → next gap +6 → 21 = U.
Ravi walks 3 km north, turns right and walks 4 km. How far is he from his starting point?
1. 5 km
2. 6 km
3. 7 km
4. 4 km
Show answer
Answer: A — 5 km
North then east are at right angles: distance = √(3² + 4²) = √25 = 5 km (the 3-4-5 triangle).
Pointing to a photo, Ram says, "She is the daughter of my grandfather's only son." How is she related to Ram?
1. Mother
2. Sister
3. Aunt
4. Daughter
Show answer
Answer: B — Sister
Grandfather's only son = Ram's father. The father's daughter = Ram's sister.
Find the odd one out: 3, 5, 7, 9, 11
1. 5
2. 7
3. 9
4. 11
Show answer
Answer: C — 9
All are prime numbers except 9 (9 = 3 × 3).
What is the angle between the hands of a clock at exactly 3:00?
1. 60°
2. 75°
3. 90°
4. 105°
Show answer
Answer: C — 90°
The hour hand moves 30° per hour; at 3:00 it is at 3 × 30° = 90° while the minute hand is at 0°.
In a certain code, MOBILE is written as NPCJMF. How is PHONE written in that code?
1. QIPOF
2. QIPNE
3. OGNMD
4. QJPOF
Show answer
Answer: A — QIPOF
Each letter shifts +1 (M→N, O→P, B→C…). So P→Q, H→I, O→P, N→O, E→F = QIPOF.
Doctor : Stethoscope :: Carpenter : ?
1. Wood
2. Saw
3. Table
4. Nail
Show answer
Answer: B — Saw
The relationship is worker to their characteristic tool: a doctor uses a stethoscope, and a carpenter uses a saw.
4 : 16 :: 5 : ?
1. 20
2. 24
3. 25
4. 30
Show answer
Answer: C — 25
The rule is "square the number": 4² = 16, so 5² = 25.
If "A × B" means A is the father of B, what does "P × Q × R" tell us about the relationship between P and R?
1. P is R's father
2. P is R's brother
3. P is R's grandfather
4. P is R's uncle
Show answer
Answer: C — P is R's grandfather
P × Q means P is the father of Q, and Q × R means Q is the father of R. So P is Q's father, and Q is R's father — one generation up from Q to P, and one generation down from Q to R — making P the grandfather of R.