Simplification – Aptitude Concepts and Formulas
For exams like Bank PO, SSC CGL, Insurance AO, Railways, and other aptitude tests, the Simplification section tests numerical ability, speed, and accuracy.
1. Basic Concepts to Revise
Candidates must be fluent with:
- BODMAS rule (Bracket → Of → Division → Multiplication → Addition → Subtraction)
- Fractions and Decimals
- Converting between them quickly
- Comparing fractions
- Percentage equivalences (½ = 50%, ⅓ = 33.33%, ⅕ = 20%, etc.)
- Reciprocal values (1/2 = 0.5, 1/3 ≈ 0.333, 1/4 = 0.25, etc.)
| Percentage (%) | Fraction | Decimal |
|---|---|---|
| 1% | $\frac{1}{100}$ | 0.01 |
| 5% | $\frac{1}{20}$ | 0.05 |
| 10% | $\frac{1}{10}$ | 0.1 |
| 12.5% | $\frac{1}{8}$ | 0.125 |
| 20% | $\frac{1}{5}$ | 0.2 |
| 25% | $\frac{1}{4}$ | 0.25 |
| 33.33% | $\frac{1}{3}$ | 0.333 |
| 50% | $\frac{1}{2}$ | 0.5 |
| 66.67% | $\frac{2}{3}$ | 0.666 |
| 75% | $\frac{3}{4}$ | 0.75 |
| 100% | 1 | 1.0 |
Reference: Percentage Decimal Fraction Conversion Table
2. Common Squares, Cubes, Powers & Roots to memorize
Square roots till 20 and cubes till 10
| Number | Square (n²) | Cube (n³) |
|---|---|---|
| 1 | 1 | 1 |
| 2 | 4 | 8 |
| 3 | 9 | 27 |
| 4 | 16 | 64 |
| 5 | 25 | 125 |
| 6 | 36 | 216 |
| 7 | 49 | 343 |
| 8 | 64 | 512 |
| 9 | 81 | 729 |
| 10 | 100 | 1000 |
| 11 | 121 | |
| 12 | 144 | |
| 13 | 169 | |
| 14 | 196 | |
| 15 | 225 | |
| 16 | 256 | |
| 17 | 289 | |
| 18 | 324 | |
| 19 | 361 | |
| 20 | 400 |
Square & Cube Roots (1 – 3)
| Number | √ n (Square Root) | ∛ n (Cube Root) |
|---|---|---|
| 1 | 1.000 | 1.000 |
| 2 | 1.414 | 1.260 |
| 3 | 1.732 | 1.442 |
Common Powers
Remember common powers will help you speed up & be more confident in the examination. You can refer the list of common powers you must memorize for the exam here
3. Simplification Techniques
- Approximations
- Rounding off decimals smartly
- Using approximate percentage values (esp. in banking exams)
- Dealing with fractions:
- Cross multiplication for comparison
- Converting mixed fractions
- Surds & Indices:
- Laws of indices (aᵐ × aⁿ = aᵐ⁺ⁿ, (aᵐ)ⁿ = aᵐⁿ, etc.)
- Simplifying √ expressions
- Digital Sum / Unit Digit Techniques:
- To find last digit or check divisibility/accuracy quickly
- Algebric manipulations
- Multiplying near base (e.g., 99×97 = (100−1)(100−3))
- using identities like 101*99 = 100^2 – 1^2
- Approximation: When exact calculation isn’t required
- Round decimals and fractions to nearest whole number
- Replace complex surds (√50 ≈ 7.07 → use 7)
Refer Aptitude Concepts
Practice Aptitude Questions on Simplification