19 Number Series, Letter Series, Codes and Relationships
This unit covers four high-frequency NTA Paper-I question types: number series, letter series, coding-decoding, and blood-and-direction relationships. Each problem rewards pattern recognition over computation.
19.1 Number Series
A number series is a sequence following a rule. The task is to identify the rule and find the missing or next term.
| Pattern | Rule | Example | Next term |
|---|---|---|---|
| Arithmetic progression | Add a constant difference | 2, 5, 8, 11, … | 14 (+3) |
| Geometric progression | Multiply by a constant ratio | 3, 6, 12, 24, … | 48 (×2) |
| Squares | n² | 1, 4, 9, 16, 25, … | 36 |
| Cubes | n³ | 1, 8, 27, 64, … | 125 |
| Fibonacci | Sum of previous two | 1, 1, 2, 3, 5, 8, … | 13 |
| Prime numbers | Only two divisors | 2, 3, 5, 7, 11, 13, … | 17 |
| Difference series | Differences form a pattern | 1, 4, 9, 16, 25 (diffs: 3, 5, 7, 9) | 36 |
| Alternating series | Two interleaved patterns | 2, 100, 4, 200, 6, 300, … | 8, 400 |
| Mixed operations | Combination of operations | 2, 5, 11, 23, 47, … | 95 (×2 + 1) |
19.1.1 Working Approach to Number Series
- Examine differences between consecutive terms.
- Examine ratios if differences don’t show a pattern.
- Check for squares, cubes, primes, Fibonacci.
- Look for alternating sub-series (every alternate term).
- Test combinations (×2 + 1, etc.).
Worked example. Find the next term: 2, 6, 12, 20, 30, ?
Differences: 4, 6, 8, 10 → next difference = 12 → next term = 30 + 12 = 42.
(Equivalently, the rule is n(n+1): 1×2, 2×3, 3×4, 4×5, 5×6, 6×7 = 42.)
19.2 Letter Series
The English alphabet (A=1, B=2, …, Z=26) is the basis of letter-series problems. Memorising the position numbers is essential.
Forward: A=1, B=2, C=3, D=4, E=5, F=6, G=7, H=8, I=9, J=10, K=11, L=12, M=13, N=14, O=15, P=16, Q=17, R=18, S=19, T=20, U=21, V=22, W=23, X=24, Y=25, Z=26.
Reverse: Z=1, Y=2, X=3, …, A=26.
Mnemonic for vowels: A, E, I, O, U → 1, 5, 9, 15, 21.
Useful midpoint: M=13, N=14 (alphabet midpoint).
| Pattern | Example | Next |
|---|---|---|
| Skip 1 letter | A, C, E, G, … | I |
| Skip 2 letters | A, D, G, J, … | M |
| Increasing skips (+1, +2, +3, …) | A, B, D, G, K, … | P |
| Reverse alphabet | Z, Y, X, W, … | V |
| Alternate forward and reverse | A, Z, B, Y, C, X, … | D, W |
| Letter + number | A1, B2, C3, … | D4 |
Worked example. Find the missing letter: B, F, K, Q, ?
Differences in position: B(2)→F(6)=+4; F(6)→K(11)=+5; K(11)→Q(17)=+6 → next +7 → 17+7 = 24 = X.
19.3 Coding-Decoding
A code is a transformation rule applied to a word. The task is to identify the rule and apply it to a new word.
| Type | Rule | Example |
|---|---|---|
| Letter shift (forward) | Each letter shifts forward by N positions | A→C, B→D, C→E (shift 2): “CAT” → “ECV” |
| Letter shift (reverse) | Each letter is replaced by mirror letter (A↔︎Z, B↔︎Y, …) | “CAT” → “XZG” |
| Number coding | Each letter replaced by its position | “CAT” = 3-1-20 |
| Reverse number coding | Each letter replaced by reverse position (Z=1) | “CAT” = 24-26-7 |
| Word substitution | Each word stands for another | “Apple is fruit” → “Mango is sweet” (apple=mango, fruit=sweet) |
| Symbol coding | Letters replaced with symbols | A=$, B=*, C=#, … |
If “CAT” is coded as “ECV”, what is “DOG” coded as?
The shift is +2 in the alphabet (C→E, A→C, T→V).
Apply +2 to “DOG”: D→F, O→Q, G→I → “FQI”.
If “BAT” is coded as “YZG”, find “FAN”.
Reverse alphabet: 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.
So F→U, A→Z, N→M → “UZM”.
19.4 Blood Relations
Blood-relation problems describe family relationships through a chain of statements; the task is to identify the relationship between two named persons.
| Relation | Description |
|---|---|
| Father / Mother | Direct parent |
| Son / Daughter | Direct child |
| Brother / Sister | Same parents |
| Grandfather / Grandmother | Parent of parent |
| Grandson / Granddaughter | Child of child |
| Uncle / Aunt | Sibling of parent |
| Nephew / Niece | Child of sibling |
| Cousin | Child of uncle / aunt |
| Father-in-law / Mother-in-law | Parent of spouse |
| Brother-in-law / Sister-in-law | Sibling of spouse, or spouse of sibling |
19.4.1 Working Approach
- Draw a family tree — males as squares, females as circles, generations as horizontal lines.
- Mark the speaker clearly.
- Trace each statement step by step.
- Identify the relation asked from the final position on the tree.
“Pointing to a man, Rita said, ‘He is the brother of my mother’s only son’s father.’ How is the man related to Rita?”
- Rita’s mother’s only son = Rita’s brother.
- The brother’s father = Rita’s father.
- The brother (the man) of Rita’s father = Rita’s uncle (paternal).
Answer: The man is Rita’s uncle.
19.5 Direction Sense
Direction problems ask the candidate to track a person’s path and determine the final position or distance.
- N · NE · E · SE · S · SW · W · NW (clockwise from North)
- Right of North = East; Left of North = West.
- Right of East = South; Right of South = West; Right of West = North.
- 90°, 180°, 270° turns map directions: e.g., facing East, 90° clockwise → South.
19.5.1 Working Approach
- Draw the path on a coordinate grid.
- Mark each step with its direction and distance.
- Use Pythagoras for diagonal distances: if East = x and North = y, total distance = √(x² + y²).
A man walks 3 km east, then 4 km north. How far is he from his starting point?
Distance = √(3² + 4²) = √(9 + 16) = √25 = 5 km. (3-4-5 right triangle.)
19.6 Ranking and Order
Ranking problems describe people’s positions in a queue or row.
- Total = Rank from front + Rank from back − 1.
- If A is kᵗʰ from front and mᵗʰ from back: Total people = k + m − 1.
- If there are N people and A is kᵗʰ from front, A is (N − k + 1)ᵗʰ from back.
In a row of 40 students, Ravi is 12th from the front. How many students are behind him?
Behind Ravi = Total − Position from front = 40 − 12 = 28 students.
19.7 Practice Questions
Find the next number in the series: 2, 6, 12, 20, 30, ?
View solution
Find the missing number: 3, 6, 12, 24, ?, 96
View solution
Find the next letter in the series: B, F, K, Q, ?
View solution
If "CAT" is coded as "ECV", what is "DOG" coded as?
View solution
If "BAT" is coded as "YZG" (reverse / mirror alphabet), what is "FAN" coded as?
View solution
Pointing to a man, Rita said, "He is the brother of my mother's only son's father." How is the man related to Rita?
View solution
A man walks 6 km east and then 8 km north. How far is he from his starting point?
View solution
In a row of children, Anita is 9th from the left and 16th from the right. How many children are in the row?
View solution
- Number-series patterns: AP, GP, squares, cubes, Fibonacci, primes, alternating, differences, mixed.
- Letter positions: A=1, M=13, N=14, Z=26; mirror pairs sum to 27.
- Coding types: Forward shift, Reverse / mirror, Number coding, Word substitution, Symbol coding.
- Blood relations: draw the family tree; mark the speaker.
- Direction: Pythagoras for diagonal — √(x² + y²); 3-4-5 and 6-8-10 triples are common.
- Ranking formula: Total = Rank from front + Rank from back − 1.