Simplification and Approximation
Overview
Simplification and Approximation is the highest-scoring topic in SBI Clerk Prelims Numerical Ability section. These questions reward speed over complexity—most involve basic arithmetic but under strict time pressure (about 20 minutes for 35 questions).
The core skill is applying BODMAS correctly while knowing when to calculate exactly versus when to round aggressively. Simplification questions demand precise answers; approximation questions expect you to estimate within 5–10% and pick the closest option. Mastering both modes is essential because the exam mixes them freely, and applying the wrong approach wastes precious seconds.
This topic requires no advanced concepts—just fluency with percentages, squares, cubes, fractions, and decimals.
Key Concepts
- BODMAS Rule: Brackets → Orders (powers, roots) → Division → Multiplication → Addition → Subtraction. Always follow this sequence strictly in simplification.
- Approximation Threshold: When a question says "approximate value" or "≈", round numbers to nearest convenient values before calculating. Typically round to nearest 5, 10, or whole number.
- Percentage-Decimal-Fraction Equivalence: Instantly convert between forms. For example, 12.5% = 1/8 = 0.125. This speeds up mixed calculations.
- Square and Cube Recognition: Identify perfect squares (1 to 30) and cubes (1 to 15) on sight. Many expressions contain hidden squares/cubes.
- Fraction Simplification: Always reduce fractions before multiplying. Cancel common factors across numerator and denominator early.
- "Of" Means Multiply: In expressions like "40% of 250", treat "of" as multiplication: 0.4 × 250.
- Decimal Alignment: When adding/subtracting decimals, mentally align decimal points. Careless misalignment causes wrong answers.
- Answer Option Spread: In approximation, check how far apart options are. Wide gaps (e.g., 450, 520, 600, 680) allow rougher estimates; close options need tighter calculation.
Formulas / Key Facts
Essential Squares (Memorize 1–30)
- 11² = 121, 12² = 144, 13² = 169, 14² = 196, 15² = 225
- 16² = 256, 17² = 289, 18² = 324, 19² = 361, 20² = 400
- 21² = 441, 22² = 484, 23² = 529, 24² = 576, 25² = 625
Essential Cubes (Memorize 1–15)
- 6³ = 216, 7³ = 343, 8³ = 512, 9³ = 729, 10³ = 1000
- 11³ = 1331, 12³ = 1728, 13³ = 2197, 14³ = 2744, 15³ = 3375
Fraction-Percentage Equivalents
- 1/2 = 50%, 1/3 ≈ 33.33%, 1/4 = 25%, 1/5 = 20%, 1/6 ≈ 16.67%
- 1/7 ≈ 14.28%, 1/8 = 12.5%, 1/9 ≈ 11.11%, 1/10 = 10%
Square Roots (Approximate)
- √2 ≈ 1.414, √3 ≈ 1.732, √5 ≈ 2.236, √7 ≈ 2.646
Useful Products
- 25 × 4 = 100, 125 × 8 = 1000, 37.5 × 8 = 300
Worked Examples
Example 1: Pure Simplification
Question: 18 × 15 + 324 ÷ 18 – 12² = ?
Step 1: Apply BODMAS — handle division and powers first
- 324 ÷ 18 = 18
- 12² = 144
Step 2: Handle multiplication
- 18 × 15 = 270
Step 3: Addition and subtraction left to right
- 270 + 18 – 144 = 288 – 144 = 144
Example 2: Approximation
Question: 39.97% of 4011 + 17.98% of 3499 = ?
Step 1: Round the percentages and numbers
- 39.97% ≈ 40%, 4011 ≈ 4000
- 17.98% ≈ 18%, 3499 ≈ 3500
Step 2: Calculate
- 40% of 4000 = 0.4 × 4000 = 1600
- 18% of 3500 = 0.18 × 3500 = 630
Step 3: Add
- 1600 + 630 = 2230
If options are 2180, 2230, 2285, 2340 → Answer is 2230
Example 3: Mixed Expression with Roots and Fractions
Question: √529 + 13³ ÷ 169 – 45% of 80 = ?
Step 1: Recognize values
- √529 = 23 (since 23² = 529)
- 13³ = 2197
- 169 = 13²
Step 2: Compute division
- 2197 ÷ 169 = 13 (since 13³ ÷ 13² = 13)
Step 3: Calculate percentage
- 45% of 80 = 0.45 × 80 = 36
Step 4: Combine
- 23 + 13 – 36 = 36 – 36 = 0
Common Mistakes
- Ignoring BODMAS in left-to-right sequences → Students compute 20 – 5 + 3 as 20 – 8 = 12 instead of correct (20 – 5) + 3 = 18. Addition and subtraction are equal priority; work left to right.
- Over-approximating in close-option questions → Rounding 7.89 to 8 and 51.2 to 50 when options differ by only 10 causes wrong picks. Check option spread first; tighten estimates for close options.
- Forgetting "of" means multiplication → Reading "25% of 60% of 400" and adding instead of multiplying. Compute as 0.25 × 0.6 × 400 = 60.
- Misreading division vs. multiplication signs → Under pressure, ÷ looks like +. Slow down for half a second on operator recognition.
- Calculating squares from scratch → Computing 17² by multiplication wastes 10+ seconds. Memorize squares up to 30; recognize them instantly.
Quick Reference
- BODMAS: Brackets → Orders → Division → Multiplication → Addition → Subtraction
- For approximation: round to nearest 5 or 10, then compute
- "Of" = × (multiplication)
- Know squares 1–30 and cubes 1–15 cold
- Check option gaps before deciding how roughly to estimate
- Addition and subtraction: equal priority, work left to right