Number & Letter Series

QUIZ

Number series questions involve identifying the hidden pattern governing the progression of numbers. Common patterns include:

1. Difference-Based Patterns

  • Consecutive differences:
    Example:
    $-1, 5, 15, 29, ?$
    Differences → $6, 10, 14, …$
    Pattern: +4 each step.
    Next difference = $18$ → Next term = $29 + 18 = 47$

2. Multiplicative Patterns

Numbers progress by multiplication or a mix of × and ± operations:
Example:
$2, 6, 18, 54, …$
Multiply ×3 each time.

3. Square, Cube & Polynomial Patterns

Some series follow:

  • $n^2$ or $n^3$
  • Alternating squares
  • Quadratic patterns

Example:
$1, 4, 9, 16, 25…$ → perfect squares.

4. Alternating Patterns

Two or more sequences interwoven: Example:
$5, 7, 12, 14, 19, 21…$

Odd terms: +7 each time
Even terms: +7 each time

5. Mix of Operations

Example:
$3, 7, 15, 31…$
Pattern: ×2 + 1

Letter Series: Core Concepts

Letter series questions follow letter-position logic based on the English alphabet:

A = 1, B = 2, C = 3 … Z = 26

1. Alphabetic Position Shifts

Example:
ABD, DGK, HMS, MTB, SBL, ?

Break each group:

  • First letters: A → D → H → M → S → ?
    Positions: 1,4,8,13,19 → increments +3,+4,+5,+6 → next +7 → 26 = Z

  • Second letters: B → G → M → T → B → ?
    Positions: 2,7,13,20,2 → increments +5,+6,+7,+8 → next +9 → 2+9=11=K

  • Third letters: D → K → S → B → L → ?
    Positions: 4,11,19,2,12 → increments +7,+8,+9,+10 → next +11
    12+11=23=W

So answer = ZKW

This pattern—a fixed incremental jump for each position—is common.

Coding-Decoding Letter Series

Coding questions modify letters using a rule. The rule may involve:

1. Forward or Backward Shifts

Example:
A → C (shift +2)

2. Mirroring Against Alphabet

Example:
A ↔ Z, B ↔ Y, C ↔ X

3. Alternating Shifts

Example:
+2, −1, +3, −2,…

4. Pattern Seen in Example from Image

“If VARANASI is coded as WCUESGZQ”

Steps typically used:

  • Each letter shifted differently
  • Pattern repeats
  • Could be:
    • +2, −4, +6, −8, …
    • Or positions reversed
    • Or vowel-consonant-based coding

To decode “KOLKATA”, apply same rule letter-by-letter.

How to Approach These Questions Quickly

1. Write Alphabet Positions

Always convert letters:
K = 11, O = 15, L = 12, A = 1, etc.

2. Check Differences

For number series → write +, −, ×, / differences.

3. Look for Consistency

Patterns rarely change mid-series.

4. Check for Alternation

If numbers behave strangely → check odd & even positions separately.

5. For Coding

Map original → coded letters and compute exact shifts.

Solved Examples

(A) Number Series

$-1, 5, 15, 29, ?$
Differences: $+6, +10, +14, …$
Increase = +4
Next diff = 18
Answer → 29 + 18 = 47

(B) Letter Series

ABD, DGK, HMS, MTB, SBL, ?
Answer → ZKW

(C) Coding-Decoding

If VARANASI → WCUESGZQ
Apply same shifts to KOLKATA.
(Final answer depends on detailed rule → taught above.)