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SBI Clerk Simplification & Approximation

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This page covers SBI Clerk Simplification & Approximation with complete concept notes, 15 graded practice MCQs, key points and exam-specific tips. Free to study.

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Concept Notes

Simplification & Approximation— Rules & Concept

Core ConceptRead this first — the foundation of the topic
Core Concept

Simplification means solving expressions step by step using BODMAS rule. Approximation means finding values close to exact answers using rounding or estimation techniques. Both skills are essential for solving complex problems in limited exam time

Follow BODMAS strictly

Brackets, Orders (powers/roots), Division, Multiplication, Addition, Subtraction 2. Simplify fractions by finding common factors 3. Convert mixed numbers to improper fractions when needed 4. Use algebraic identities wherever possible Approximation Techniques: 1.

Round numbers to nearest 10, 100, or simple fractions 2. Use estimation for quick elimination of wrong options 3. Apply percentage approximations for decimal calculations

Formula BlockMemorise — at least one formula appears in every paper
• (a + b)² = a² + 2ab + b²
• (a - b)² = a² - 2ab + b²
• a² - b² = (a + b)(a - b)
• (a + b + c)² = a² + b² + c² + 2(ab + bc + ca)
• √(ab) = √a × √b
• Percentage approximation: 0.33 ≈ 1/3, 0.25 = 1/4, 0.125 = 1/8
Exam PatternsWhat examiners ask — read before attempting PYQs

SSC CGL typically asks 3-5 direct simplification questions worth 6-10 marks. Questions involve complex fractions, square roots, percentages, and mixed operations. Time allocation should be maximum 1-2 minutes per question. Powerful Shortcut - Fraction Multiplication Trick: When multiplying fractions, cancel common factors diagonally before multiplying. This reduces calculation time by 50%.

Worked ExampleSolve this step-by-step before moving on
1
Step 1

Convert decimals to fractions = (24/10 × 16/10 × 5/10) / (8/10 × 3/10 × 4/1)

2
Step 2

Simplify by canceling = (24 × 16 × 5) / (10 × 8 × 3 × 4 × 10)

3
Step 3

Cancel common factors 24/8 = 3, 16/4 = 4, 5 cancels with denominator = (3 × 4) / (10 × 3 × 10) = 12/300 = 1/25 = 0.04 Worked Example 2: Approximate: √624 + √1444

1
Step 1

Find perfect squares nearby √624 ≈ √625 = 25 (since 625 = 25²) √1444 ≈ √1444 = 38 (since 38² = 1444)

2
Step 2

Add approximated values 25 + 38 = 63 Exact calculation gives 62.98, so approximation is highly accurate. Mega Shortcut - Options Elimination: In MCQs, approximate the answer first. Eliminate options that are far from your approximation. Then calculate precisely only for remaining close options. The #1 Most Common Trap: Students ignore BODMAS order and calculate left to right. For expression 2 + 3 × 4, wrong approach gives (2 + 3) × 4 = 20. Correct answer following BODMAS: 2 + (3 × 4) = 14. This single mistake can cost 2-4 marks in the exam. Another critical error is incorrect fraction handling. When adding fractions with different denominators, students often add numerators and denominators separately instead of finding LCM first.

Key Points to Remember

  • BODMAS rule is mandatory: Brackets → Orders → Division → Multiplication → Addition → Subtraction
  • Shortcut: (a + b)² = a² + 2ab + b² saves calculation time in complex expressions
  • Approximation formula: Round to nearest easy numbers first, then calculate
  • Fraction multiplication trick: Cancel common factors diagonally before multiplying
  • Time management: Spend maximum 1-2 minutes per simplification question
  • Options elimination: Use approximation to eliminate obviously wrong answers
  • Decimal conversion: 0.25 = 1/4, 0.33 = 1/3, 0.125 = 1/8, 0.2 = 1/5
  • Square root estimation: Memorize perfect squares 1² to 30² for quick approximation
  • Percentage shortcut: 10% of any number = number/10, 1% = number/100
  • Common trap: Never calculate left to right, always follow BODMAS strictly

Exam-Specific Tips

  • Perfect squares to memorize: 25² = 625, 26² = 676, 27² = 729, 28² = 784, 29² = 841, 30² = 900
  • Cube roots: ∛125 = 5, ∛216 = 6, ∛343 = 7, ∛512 = 8, ∛729 = 9, ∛1000 = 10
  • Fraction decimals: 1/7 = 0.142857 (repeating), 1/9 = 0.111... (repeating), 1/11 = 0.090909...
  • Value of √2 = 1.414, √3 = 1.732, √5 = 2.236 for approximation purposes
  • Percentage equivalents: 12.5% = 1/8, 16.67% = 1/6, 37.5% = 3/8, 62.5% = 5/8
  • Powers of 2: 2⁶ = 64, 2⁷ = 128, 2⁸ = 256, 2⁹ = 512, 2¹⁰ = 1024
  • Common algebraic identity: (a + b)³ = a³ + b³ + 3ab(a + b)
  • Simplification weights 8-12% of total Quantitative Aptitude marks in SSC CGL
Practice MCQs

Simplification & Approximation — Practice Questions

15graded MCQs · easy to hard · full solution & trap analysis

All MCQs →
Practice 1easy

What is 35% of 240?

Practice 2easy

Approximate: √625 + ∛216 − 5²

Practice 3easy

Simplify: (18 + 12) ÷ 6 + 8 − 3

Practice 4easy

What is 48% of 150?

Practice 5easy

Simplify: 100 − 36 ÷ 4 + 2 × 5

Practice 6easy

Simplify: 45 ÷ 9 + 12 × 2 − 8

Practice 7medium

Simplify: (48 × 5) ÷ (16 + 4) + 18 ÷ 3 − 2

Practice 8medium

What is the approximate value of √625 + ∛216 − 2³?

Practice 9medium

If 3⁴ + 2⁵ − 5² = x, then what is the value of x ÷ 4?

Practice 10medium

Simplify: (√144 + √169) × (√100 − √64) ÷ 2

Practice 11medium

Simplify: (144 ÷ 12) × 8 + 56 ÷ 7 − 3 × 4

Practice 12hard

If a number is increased by 25%, and then decreased by 20%, what is the net percentage change?

Practice 13hard

Simplify: (√625 × ∛216 + 144 ÷ 12) / (5² - 3²). What is the approximate value?

Practice 14hard

Simplify: (2⁶ × 3⁴) / (2⁴ × 3²) + √144 - 5. What is the result?

Practice 15hard

If 40% of a number is 240, what is 65% of that number?

60-Second Revision — Simplification & Approximation

  • Remember: BODMAS rule prevents 80% of calculation errors in simplification
  • Formula: Use (a + b)² = a² + 2ab + b² for quick expansion calculations
  • Trap: Never add fractions by adding numerators and denominators separately
  • Shortcut: Cancel common factors diagonally in fraction multiplication
  • Strategy: Approximate first, eliminate wrong options, then calculate precisely
  • Time-saver: Memorize perfect squares 1² to 30² and cubes 1³ to 10³
  • Key conversion: 0.125 = 1/8, 0.25 = 1/4, 0.33 = 1/3, 0.75 = 3/4
←Fractions & DecimalsBODMAS→
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