Rajasthan TET – Reasoning Ability
Coding‑Decoding
Coding‑Decoding problems test your ability to detect and apply patterns, relationships, or rules that “encode” data into a different form (numbers, letters, symbols, or shapes) and then “decode” them back.
They are common in aptitude tests, entrance exams, and placement tests.
1. Simple Explanation
| Step | What to Do | Example |
|---|---|---|
| 1. Observe | Write down the data (numbers, letters, symbols). | 3, 7, 11, 15, 19 |
| 2. Look for a rule | Check differences, ratios, positions, or any mathematical/linguistic pattern. | Differences = +4 each step |
| 3. Encode or decode | If the question gives the rule, encode the next item. If it gives a coded form, decode it to the original. | Next number = 19 + 4 = 23 |
| 4. Verify | Ensure the rule holds for all given items. | 3→7 (+4), 7→11 (+4), … |
Rule = “the key” that transforms one form into another.
2. Key Points
| Category | What to remember |
|---|---|
| Types of Coding‑Decoding | 1. Numerical patterns (arithmetic, geometric, Fibonacci, alternating). 2. Alphabetic patterns (A=1, Z=26; reverse order; skip letters). 3. Symbolic patterns (shapes, colors, numbers on a clock). |
| Common Patterns | • Arithmetic Series – constant difference. • Geometric Series – constant ratio. • Alternating Pattern – two or more sub‑patterns interleaved. • Skip Pattern – skip one, two, or more items. • Reverse/Palindrome – sequence reads the same backward. |
| Coding vs Decoding | • Coding: Set a rule (e.g., “add 3”) and apply it to a base value. • Decoding: Apply the inverse rule (e.g., “subtract 3”) to a coded value. |
| Check for Multiple Rules | If one rule doesn’t fit all data, look for a different rule for a subset. |
| Time Management | Quickly identify the simplest rule first; if stuck, move to the next possible pattern. |
| Common Pitfalls | • Assuming arithmetic when a geometric rule applies. • Ignoring special cases like “0, 1, 1, 2, 3, 5” (Fibonacci). • Forgetting to reverse the rule for decoding. |
3. Worked Example
Question (Typical of Rajasthan TET)
In a series the numbers are coded as follows:
4 → B
5 → C
6 → D
7 → E
8 → F
9 → G
What is the code for 13?
Step‑by‑Step Solution
| Step | Explanation | Calculation |
|---|---|---|
| 1. Observe | Sequence of numbers 4–9 mapped to letters B–G. | — |
| 2. Find the rule | The mapping is number → corresponding alphabet letter where A=1. Thus 4 = D, 5 = E, etc. But the given mapping starts from B, meaning the numbers have been shifted by +1. | |
| 3. Encode 13 | Convert 13 → M (since A=1, M=13). | |
| 4. Adjust for shift | Shift back by 1 (since the given mapping is +1), so 13 → L. | |
| Result | Code for 13 is L. |
Quick Check
- 4→B (B is the 2nd letter, 4‑2 = 2 → shift +1).
- 9→G (G is 7th, 9‑7 = 2 → shift +1).
Thus the rule holds.
4. Quick Revision Summary
| Topic | What to remember |
|---|---|
| Identify the base | Numbers, letters, symbols, or shapes. |
| Look for simple arithmetic | Constant difference (+, −, ×, ÷). |
| Look for simple geometric | Constant ratio or power. |
| Look for alternating or skip patterns | Two or more interleaved sub‑series. |
| Check alphabetic mapping | A=1, B=2, …, Z=26; consider shifts or reverses. |
| Decoding rule | Apply inverse of the coding rule. |
| Time‑saving tip | Try the most common patterns first; if no match, try others. |
| Common mistakes | Mis‑identifying the rule, ignoring special cases, forgetting to reverse for decoding. |
Practice Tip:
Solve at least 5 coding‑decoding problems daily, covering both simple arithmetic patterns and alphabetic mappings. Time yourself and review the solutions to spot patterns quickly.