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NDA Simplification & Approximation

Study Material — 22 PYQs (2018–2023) · Concept Notes · Shortcuts

NDA Simplification & Approximation is a frequently tested subtopic — 22 previous year questions from 2018–2023 papers are included below with concept notes, key rules and shortcut tricks.

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Previous Year Questions

NDA Simplification & Approximation — Past Exam Questions

22 questions from actual NDA papers · all shown free · click option to reveal solution

Exam Q 12023Previous Year Pattern

What is the value of √256 + √144 − √100?

Exam Q 22023Previous Year Pattern

What is the value of √256 + ∛27 − √100?

Exam Q 32023Previous Year Pattern

Simplify: (144 ÷ 12) × 5 + 18 ÷ 3 − 8

Exam Q 42023Previous Year Pattern

If 3/5 of a number is 45, what is the number?

Exam Q 52023Previous Year Pattern

Simplify: (7² − 5²) ÷ (7 + 5)

Exam Q 62023Previous Year Pattern

What is 25% of 320?

Exam Q 72020Previous Year Pattern

Simplify: (144 ÷ 12) × 5 + 36 ÷ 6 − 8

Exam Q 82023Previous Year Pattern

Simplify: (8 × 15) ÷ (6 × 4) + 12

Exam Q 92023Previous Year Pattern

Simplify: (8 × 9) ÷ (6 ÷ 2) + 5

Exam Q 102018Previous Year Pattern

Simplify: 1248 ÷ 26 × 4 – 120 + 35

Exam Q 112023Previous Year Pattern

Simplify: [48 ÷ 6 + 12 × 2 - (18 - 6)] ÷ 5

Exam Q 122023Previous Year Pattern

If 40% of a number is 96, what is 65% of that number?

Exam Q 132023Previous Year Pattern

A number when divided by 8 gives quotient 15 and remainder 3. What is the number?

Exam Q 142023Previous Year Pattern

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

Exam Q 152023Previous Year Pattern

A number when divided by 12 gives a quotient of 18 and a remainder of 7. What is the number?

Exam Q 162023Previous Year Pattern

If (2⁵ × 3⁴ × 5²) ÷ (2³ × 3² × 5) = 2^a × 3^b × 5^c, then find the value of (a + b + c).

Exam Q 172023Previous Year Pattern

Simplify: [∛(1728) + ∛(512)] ÷ [∛(343) - ∛(125)] × ∛(64)

Exam Q 182023Previous Year Pattern

Simplify: (144 ÷ 12 + 8) × (15 - 3 × 2) ÷ (20 - 5 × 3)

Exam Q 192023Previous Year Pattern

Simplify: (√625 × ∛216) ÷ (√144 + √169) + 5²

Exam Q 202023Previous Year Pattern

Simplify: [(2⁴ × 3³) ÷ (2² × 3)] × (2 × 3²) ÷ (2³ × 3)

Exam Q 212020Previous Year Pattern

Simplify: √(1296) + ∛(1728) − ⁴√(256) + (0.5)⁻² − 2³

Exam Q 222023Previous Year Pattern

If 40% of a number is 240, and 60% of another number is 360, then what is the ratio of the first number to the second number?

Concept Notes

Simplification & Approximation— Rules & Concept

1.Core Concept

Read this first — the foundation of the topic

SIMPLIFICATION & APPROXIMATION — COMPLETE GUIDE FOR SSC CGL ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

CORE CONCEPT ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

Simplification means finding the exact answer of a mathematical expression. Approximation means finding a value that is very close to the correct answer — not exact, but near enough to pick the right option. In SSC CGL, Simplification questions ask you to solve expressions using correct order of operations. Approximation questions give you messy decimals or roots and ask you to find the nearest value. Together, these two question types appear in almost every paper.

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ KEY RULE — BODMAS

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ BODMAS tells you the correct ORDER to solve any expression:

B — Brackets (solve innermost first: round, then curly, then square) O — Of (means multiplication: 'of' = x)

D — Division M — Multiplication

A — Addition S — Subtraction

IMPORTANT: Division and Multiplication have EQUAL priority — solve left to right. Same rule for Addition and Subtraction. ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

2.Formula Block

Memorise — at least one formula appears in every paper
(a + b)^2 = a^2 + 2ab + b^2
(a - b)^2 = a^2 - 2ab + b^2
a^2 - b^2 = (a + b)(a - b)
(a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3
a^3 + b^3 = (a + b)(a^2 - ab + b^2)
a^3 - b^3 = (a - b)(a^2 + ab + b^2)

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

Useful identities to speed up calculation:

For approximation:

Round each number to nearest convenient value, then calculate.

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

3.Exam Patterns

What examiners ask — read before attempting PYQs
Approximation

3847.99 / 39.02 x 4.98 = ? 5. Finding missing numbers (? box) in an expression ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ SHORTCUTS AND TRICKS ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ TRICK 1 — APPROXIMATION ROUNDING RULE: Round all numbers to the nearest whole number or simple fraction. Then calculate. Error stays under 2% for SSC options

Example

3847.99 / 39.02 x 4.98 → treat as 3848 / 39 x 5 = 98.67 x 5 = 493.3 → nearest option

TRICK 2 — UNIT DIGIT SHORTCUT FOR SIMPLIFICATION

When options are far apart, just find the unit digit of the answer to eliminate wrong options. No need to fully calculate

Example

13^4 → unit digit of 3^4 = 81 → unit digit is 1. Eliminate all options not ending in 1

TRICK 3 — FRACTION CANCELLATION

In expressions like (a x b x c) / (d x e), cancel common factors before multiplying. This saves 60% calculation time. ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

4.Worked Example

Solve this step-by-step before moving on
1
Step 1

Solve innermost round bracket first. (8 - 6 + 3) = (2 + 3) = 5

2
Step 2

Now solve curly bracket. {4 - 5} = -1

3
Step 3

Now solve square bracket. [6 - (-1)] = [6 + 1] = 7

4
Step 4

Final answer. 18 - 7 = 11 Answer: 11 ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ WORKED EXAMPLE 2 — APPROXIMATION ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ Question: Approximate: 624.98 / 24.97 + 19.03 x 4.98 = ?

1
Step 1

Round the values. 625 / 25 + 19 x 5

2
Step 2

Solve division first. 625 / 25 = 25

3
Step 3

Solve multiplication. 19 x 5 = 95

4
Step 4

Add. 25 + 95 = 120 Answer: Approximately 120 (match to nearest option) ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

5.Exam Traps

Common mistakes students make — avoid these

— THE #1 TRAP ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ Students solve brackets from OUTSIDE to INSIDE instead of INSIDE to OUTSIDE. This is the single biggest error in simplification questions. Always solve the deepest/innermost bracket first, then move outward.

Also, students often ignore that subtraction of a negative number becomes addition — example: 6 - (-1) = 7, NOT 5. Memorise: minus of minus = plus.

Key Points to Remember

  • BODMAS order: Brackets → Of → Division → Multiplication → Addition → Subtraction — never skip or reorder
  • Always solve the INNERMOST bracket first, then move outward layer by layer
  • Division and Multiplication have equal priority — when both appear, solve LEFT to RIGHT
  • Addition and Subtraction have equal priority — when both appear, solve LEFT to RIGHT
  • SHORTCUT: For approximation, round each number to the nearest easy whole number or simple fraction
  • SHORTCUT: Use unit digit trick to eliminate wrong options — saves full calculation time
  • FORMULA: a^2 - b^2 = (a+b)(a-b) — use to quickly factorise and cancel in simplification
  • SHORTCUT: Cancel common factors in numerator and denominator BEFORE multiplying fractions
  • Minus of a minus equals plus — example: 10 - (-4) = 14, a very common trap in bracket questions
  • In approximation, if rounding makes one number bigger, try to round the next number slightly smaller to keep the error balanced

Exam-Specific Tips

  • BODMAS stands for Brackets, Of, Division, Multiplication, Addition, Subtraction — this is the universally accepted order of operations for Indian competitive exams
  • The three types of brackets in order of solving are: ( ) round bracket first, then { } curly bracket, then [ ] square bracket
  • a^3 + b^3 = (a + b)(a^2 - ab + b^2) — this identity is directly used in simplification questions to cancel terms
  • a^3 - b^3 = (a - b)(a^2 + ab + b^2) — note the middle term is POSITIVE ab, a common confusion point
  • Unit digits of powers follow a cycle: unit digit of 3^n cycles as 3,9,7,1 (cycle of 4); unit digit of 7^n cycles as 7,9,3,1 (cycle of 4)
  • For approximation in SSC CGL, the acceptable rounding error is typically within 2-3% of the actual answer — options are spaced far enough apart
  • Square of numbers ending in 5: (a5)^2 = a(a+1) followed by 25 — example: 75^2 = 7x8 followed by 25 = 5625
Practice MCQs

Simplification & Approximation — Practice Questions

23graded MCQs · easy to hard · full solution & trap analysis · showing 20 of 23

All MCQs →
Practice 1easy

Simplify: 3² + 4² − 5

Practice 2easy

If 15 × 8 ÷ 4 + 12 = ?, what is the answer?

Practice 3easy

What is 40% of 250?

Practice 4easy

What is the value of √256 + √144 − √100?

Practice 5easy

Simplify: (25 × 4) ÷ (100 ÷ 10) + 6

Practice 6easy

Simplify: (144 ÷ 12) × 5 + 18 ÷ 3 − 4

Practice 7easy

Simplify: (144 ÷ 12) × 5 + 18 − 6 ÷ 2

Practice 8easy

Simplify: (8 + 2) × 3 ÷ 2 + 5

Practice 9easy

Simplify: (144 ÷ 12) × 5 + 18 ÷ 3 − 8

Practice 10easy

Simplify: 1296 ÷ 36 × 4 + 125 − 78

Practice 11medium

Simplify: (2⁵ × 3⁴) ÷ (2³ × 3²) + 12 = ?

Practice 12medium

If the ratio of two numbers is 7:5 and their difference is 18, what is the larger number?

Practice 13medium

Simplify: (√625 + √441) × (√256 - √169) ÷ (√144 + √121)

Practice 14medium

If 40% of a number is 96, what is 65% of that number?

Practice 15hard

If (3⁵ - 3⁴) × (2⁶ ÷ 2⁴) = k, then what is the value of k ÷ 12?

Practice 16hard

Simplify: (√625 × ∛216 − 24) ÷ (√144 − 2) + 15% of 80

Practice 17hard

If (6⁴ ÷ 6²) + (4³ - 4²) = m, then what is m ÷ 48?

Practice 18hard

Simplify: (√625 × ∛216) ÷ (2⁴ - 2³) + 5² = ?

Practice 19hard

If x = (2⁷ + 2⁶ + 2⁵) ÷ 7, then what is the value of 14x?

Practice 20hard

Simplify: (√625 × ∛216 + 144 ÷ 12) / (5² - 3²)

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60-Second Revision — Simplification & Approximation

  • Remember: BODMAS — solve Brackets (inside out), then Of, then Division/Multiplication (left to right), then Addition/Subtraction (left to right)
  • Trap: NEVER solve outer bracket before inner bracket — always go deepest first or you will get the wrong answer
  • Trap: Minus of minus = Plus — example 8 - (-3) = 11 not 5 — this appears in almost every bracket question
  • Formula: a^2 - b^2 = (a+b)(a-b) and a^3 - b^3 = (a-b)(a^2+ab+b^2) — memorise for instant factorisation
  • Shortcut: In approximation questions, round to the nearest convenient number first, calculate, then match to closest option
  • Shortcut: Use unit digit method to eliminate 2-3 wrong options quickly without full calculation — saves 30-40 seconds per question
  • Remember: Cancel common factors in fractions BEFORE multiplying — never multiply first then cancel, it wastes time and risks errors
←Fractions & DecimalsBODMAS→
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