Number Series and Simplification: Quick Tricks for Competitive Exams
Master number series patterns and simplification shortcuts for SSC, Banking, and Railway exams with pattern recognition techniques and practice approach.
Number Series and Simplification are the two topics where speed matters more than knowledge. The concepts are straightforward — you learned them in school. But solving 5 number series questions in 3 minutes or simplifying complex expressions in 30 seconds each? That requires a specific type of practice that most aspirants neglect.
Together, these topics contribute 8–12 questions in Banking exams and 3–5 questions in SSC exams. They're also the most time-efficient questions to attempt — if you've trained your pattern recognition and calculation speed.
Number Series: Pattern Types
Every number series question follows one of these patterns. Once you recognize which type it is, the answer becomes mechanical.
Type 1: Constant Difference Series
The difference between consecutive terms is the same.
Example: 3, 7, 11, 15, 19, ?
Difference: +4 each time. Answer: 23.
This is too simple for most exams, but it appears as a starting point for more complex patterns.
Type 2: Increasing/Decreasing Difference
The difference between terms itself forms a pattern.
Example: 2, 5, 11, 20, 32, ?
Differences: 3, 6, 9, 12 → next difference is 15. Answer: 47.
Type 3: Multiplication/Division Series
Each term is obtained by multiplying or dividing the previous term.
Example: 4, 12, 36, 108, ?
Each term × 3. Answer: 324.
Type 4: Square/Cube-Based Series
Terms are related to perfect squares or cubes.
Example: 1, 4, 9, 16, 25, ? → Perfect squares. Answer: 36.
Example: 2, 9, 28, 65, ? → (1³+1), (2³+1), (3³+1), (4³+1). Answer: 126 (5³+1).
Type 5: Combination Patterns
The operation alternates or combines multiple operations.
Example: 3, 5, 10, 12, 24, 26, ?
Pattern: +2, ×2, +2, ×2, +2, ×2. Answer: 52.
Type 6: Two-Tier Operations
Example: 5, 6, 14, 45, 184, ? Check: 5×1+1=6, 6×2+2=14, 14×3+3=45, 45×4+4=184, 184×5+5=925. Recognition: When simple differences and ratios don't work, try (previous term × n + n) or (previous term × n ± constant) where n increases by 1 each step.Type 7: Wrong Number in Series
Banking exams often give a series where one number is wrong. You need to identify it.
Approach:- First identify the pattern (as above).
- Check which term breaks the pattern.
- Calculate what the correct term should be.
Number Series Strategy for the Exam
Step 1: Calculate the differences between consecutive terms. If they're constant → Type 1. If they form a pattern → Type 2. Step 2: If differences seem random, check ratios between consecutive terms. If they form a pattern → Type 3. Step 3: If neither works, check if terms are close to perfect squares, cubes, or factorials. Step 4: If still stuck, try combination patterns (alternating operations). Step 5: If nothing clicks in 45 seconds, mark the question and move on. Don't spend 2 minutes on a single series question.Simplification: Speed Techniques
Simplification questions test calculation speed, not mathematical knowledge. You know how to add, subtract, multiply, and divide. The question is: can you do it fast enough?
Technique 1: BODMAS Shortcuts
Before calculating, simplify the expression mentally:
- Cancel common factors early
- Convert percentages to fractions (37.5% = 3/8, 62.5% = 5/8)
- Round numbers for estimation, then match with closest option
Technique 2: Approximation
Most simplification questions in Banking exams have well-separated options (e.g., 235, 312, 478, 521, 645). You don't need the exact answer — you need to be in the right ballpark.
Example: 39.97% of 749.8 + 24.9% of 400.2 = ?Approximate: 40% of 750 + 25% of 400 = 300 + 100 = 400. Look for the option closest to 400.
Technique 3: Fraction-Percentage Equivalents
Memorize these — they save 10–15 seconds per question:
| Fraction | Percentage | Fraction | Percentage |
|---|---|---|---|
| 1/2 | 50% | 1/8 | 12.5% |
| 1/3 | 33.33% | 1/9 | 11.11% |
| 1/4 | 25% | 1/11 | 9.09% |
| 1/5 | 20% | 1/12 | 8.33% |
| 1/6 | 16.67% | 1/15 | 6.67% |
| 1/7 | 14.28% | 1/16 | 6.25% |
Technique 4: Multiplication Shortcuts
Multiplying by 11: 23 × 11 → Write the digits with their sum in between: 2_(2+3)_3 = 253. Multiplying by 25: Divide by 4, multiply by 100. So 48 × 25 = 48/4 × 100 = 1200. Multiplying by 99: Multiply by 100 and subtract the number. 47 × 99 = 4700 - 47 = 4653. Squaring numbers ending in 5: 35² → First digit × (first digit + 1), then append 25. 3 × 4 = 12, append 25 → 1225.Technique 5: Division Shortcuts
Dividing by 5: Multiply by 2, divide by 10. So 340/5 = 680/10 = 68. Dividing by 25: Multiply by 4, divide by 100. So 625/25 = 2500/100 = 25. Dividing by 8: Divide by 2 three times. 168/8 → 84 → 42 → 21.Squares and Cubes to Memorize
You should know these cold:
Squares: 1² through 30² (1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625, 676, 729, 784, 841, 900) Cubes: 1³ through 15³ (1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, 1331, 1728, 2197, 2744, 3375)Knowing these lets you instantly recognize square/cube-based number series and speeds up simplification calculations.
Practice Plan
Week 1–2: Build Calculation Speed- Practice 20 simplification questions daily (timed: 15 minutes for 20 questions)
- Memorize fraction-percentage equivalents
- Practice multiplication tables 2–20 daily (yes, write them out)
- Solve 10 number series questions daily from PYQs
- After solving, categorize each into the 7 types listed above
- Track which types you find difficult and practice those extra
- Set a timer: 5 number series in 3 minutes, 10 simplification in 7 minutes
- If you can't hit these benchmarks, your calculation speed needs more work
Recommended Resources
- Fast Track Objective Arithmetic by Rajesh Verma (Arihant) — Good for building speed techniques
- Quantitative Aptitude for Competitive Examinations by RS Aggarwal — Comprehensive practice problems
- Testbook / Oliveboard daily quizzes — Free daily number series and simplification practice
- PYQs from IBPS PO, SBI PO, SSC CGL (2020–2025) — The patterns repeat
The Bottom Line
Number Series and Simplification are the low-hanging fruit of Quantitative Aptitude. They don't require deep mathematical understanding — they require pattern recognition and calculation speed, both of which improve predictably with consistent practice.
An aspirant who spends 30 minutes daily on calculation speed drills for 4 weeks will see a measurable improvement. This isn't motivational talk — it's a verifiable fact. Timed practice forces your brain to find shortcuts.
Check SarkariNaukri.in for the latest exam notifications and pattern changes. The number of simplification questions has fluctuated across recent IBPS and SBI exam cycles, and staying informed helps you allocate preparation time wisely.