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RRB NTPC Simplification & Approximation

Study Material — 1 PYQs (2018–2018) · Concept Notes · Shortcuts

RRB NTPC Simplification & Approximation is a frequently tested subtopic — 1 previous year questions from 2018–2018 papers are included below with concept notes, key rules and shortcut tricks.

1 PYQs
2018–2018
35 Practice
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10 Key Points
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Previous Year Questions

RRB NTPC Simplification & Approximation — Past Exam Questions

1 questions from actual RRB NTPC papers · all shown free · click option to reveal solution

Exam Q 12018Previous Year Pattern

Simplify: (2⁵ × 3⁴ × 5²) / (2³ × 3² × 5) + √(144 + 81) - 12

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

35graded MCQs · easy to hard · full solution & trap analysis · showing 20 of 35

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Practice 1easy

If 3x + 15 = 45, what is the value of x?

Practice 2easy

Simplify: √256 + √144 − √100

Practice 3easy

What is the value of √256 + √121 − √64?

Practice 4easy

What is 25% of 320?

Practice 5easy

Simplify: (144 ÷ 12) × 5 + 18 ÷ 3 − 8

Practice 6easy

What is the approximate value of √625 + ∛216 − 5?

Practice 7easy

Simplify: (144 ÷ 12) × 5 + 18 ÷ 3 − 8

Practice 8easy

If 8 × 9 = 72, then what is 72 ÷ 8?

Practice 9easy

Simplify: 3² + 4² − 5

Practice 10easy

Simplify: (72 × 5) ÷ 8 + 9 × 2 − 15

Practice 11easy

Simplify: (72 ÷ 8) + (56 ÷ 7) × 2 − 3

Practice 12easy

What is 15% of 240?

Practice 13easy

Simplify: (25 × 4) ÷ (20 ÷ 5) + 12

Practice 14easy

Approximate the value of (256 ÷ 16) × 3 + 12 ÷ 4 − 2

Practice 15medium

Simplify: (256 ÷ 16) + (81 ÷ 9) × (100 ÷ 10) - 5

Practice 16medium

Approximate: (15% of 320) + (25% of 200) - (10% of 150)

Practice 17medium

Approximate: √(625) + ∛(512) - √(196)

Practice 18medium

Simplify: (2⁶ × 3⁴) ÷ (2⁴ × 3²) + 15

Practice 19medium

What is the approximate value of √(625) + ∛(512) − √(144)?

Practice 20medium

Simplify: (2³ × 3²) ÷ (2² × 3) + 5

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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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