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SBI PO Simplification & Approximation

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This page covers SBI PO Simplification & Approximation with complete concept notes, 16 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

16graded MCQs · easy to hard · full solution & trap analysis

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Practice 1easy

Simplify: (8² − 4²) ÷ (6 − 2) + 10

Practice 2easy

If 5 × 12 ÷ 3 − 8 + 6 = ?, what is the value?

Practice 3easy

Simplify: (144 ÷ 12) × 5 + 18 ÷ 3 − 8

Practice 4easy

What is the value of √256 + ∛27 − 5?

Practice 5easy

Simplify: (72 ÷ 8) + (15 × 2) ÷ 6 + 4

Practice 6easy

What is 40% of 250 + 30% of 200?

Practice 7medium

What is the approximate value of (48% of 650) + (35% of 420) − (22% of 300)?

Practice 8medium

Simplify: [144 ÷ 12 + 8 × 3 − (15 − 6)] ÷ 5 = ?

Practice 9medium

If 35% of a number is 245, what is 48% of that number?

Practice 10medium

A shopkeeper marks an item at ₹800. He gives a 15% discount and then adds 18% GST on the discounted price. What is the final price?

Practice 11hard

A number when divided by 8 gives quotient 45 and remainder 3. If this number is multiplied by 2 and then divided by 16, what is the approximate quotient?

Practice 12hard

Simplify: [144 ÷ 12 + (15 - 8) × 2] / [√256 - 4] and approximate the result.

Practice 13hard

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

Practice 14hard

If (2⁴ × 3³ × 5²) / (2² × 3 × 5) is simplified, what is the result when multiplied by 0.5?

Practice 15hard

If 40% of a number is 240, then 60% of that number is approximately:

Practice 16hard

Approximate: (√484 + √361) × (∛343 - ∛125) / 12

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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