INSPIRE Scholarship – General Aptitude & Reasoning
Topic: Number Series & Coding‑Decoding
Goal: Master the patterns that govern numeric sequences and the logic behind coding–decoding questions, enabling quick, accurate answers in exams.
1. Simple Explanation
| What | Why | How |
|---|---|---|
| Number Series | Tests pattern recognition, arithmetic/logic skills, and speed. | Identify the rule that generates the next term. |
| Coding‑Decoding | Checks the ability to translate between two sets of symbols/letters and numbers. | Find the mapping rule (alphabet‑to‑number, positional, etc.) and apply it consistently. |
2. Key Points to Remember
| Aspect | Key Take‑aways |
|---|---|
| Common Series Patterns | 1. Arithmetic Progression – constant difference. 2. Geometric Progression – constant ratio. 3. Fibonacci‑type – sum of previous two terms. 4. Alternating Patterns – two interleaved sub‑series. 5. Square/Cube – terms are perfect squares/cubes. 6. Prime/Composite – primes or composites. 7. Digit / Position based – e.g., 1, 11, 21, 1211 (look‑and‑say). |
| Common Coding Rules | 1. Direct Alphabet‑to‑Number (A=1, B=2, …). 2. Alphabet‑to‑Number ± Offset (A=3, B=4, …). 3. Reverse Alphabet (A=26, B=25, …). 4. Pattern of Positions (odd terms → 1, even terms → 2, etc.). 5. Symbolic Substitution (★→5, ♣→10, etc.). |
| Problem‑Solving Steps | 1. Read Carefully – note if the series is linear, exponential, or alternating. 2. Check First Two Terms – often enough to spot the rule. 3. Test Hypotheses – apply a rule, verify with all given terms. 4. Look for Repeated Blocks – e.g., 5 7 5 7… 5. Use Logical Deductions – if values are too large for AP, maybe GP or digit‑sum. |
| Time Management | 1. 30 % of total time – practice recognizing patterns. 2. 10 % of total time – double‑check the answer. |
| Common Pitfalls | - Assuming a rule that fits only the first few terms. - Forgetting to check for alternate patterns. - Mixing up “coding” with “decoding” (apply reverse). |
3. Worked Example
3.1 Number Series
Series: 2, 6, 12, 20, 30, ?
Step‑by‑Step:
-
Compute Differences:
- 6 − 2 = 4
- 12 − 6 = 6
- 20 − 12 = 8
- 30 − 20 = 10
-
Look at the Differences: 4, 6, 8, 10 → Arithmetic progression with difference 2.
-
Predict Next Difference: 10 + 2 = 12
-
Add to Last Term: 30 + 12 = 42
Answer: 42
3.2 Coding‑Decoding
Question:
If the code for “B” is
4, for “C” is6, and for “D” is8, what is the code for “H”?
Observations:
| Letter | Alphabet Position | Code |
|---|---|---|
| B | 2 | 4 |
| C | 3 | 6 |
| D | 4 | 8 |
Pattern: Code = 2 × Alphabet Position
Apply to H (8th letter):
Code = 2 × 8 = 16
Answer: 16
4. Quick Revision Summary
| Topic | What to Recall | Tip |
|---|---|---|
| Number Series | Identify AP, GP, Fibonacci, alternating, square/cube, digit‑sum patterns. | Practice with 5‑term series; try to spot two sub‑series first. |
| Coding‑Decoding | Map letters to numbers via: direct, offset, reverse, position, or symbolic patterns. | Write a quick table of the first 5 letters and test each rule. |
| Problem Solving Flow | 1️⃣ Read → 2️⃣ Spot rule → 3️⃣ Verify with all terms → 4️⃣ Compute answer → 5️⃣ Double‑check. | Use a 30–second mental “rule‑check” before writing. |
| Speed Hacks | 1️⃣ Memorize common series patterns. 2️⃣ Keep a mental “code‑rule” list. 3️⃣ Skip impossible large values. |
Do timed drills: 5 min, 5 questions. |
Final Practice Question
Series:
3, 9, 15, 21, ?
Coding:X → 24, Y → 25, Z → 26. What is the code forA?
Answer in the next session!
Feel free to practice more with varied series and coding rules to build confidence and speed. Happy studying!