1. Number System, Simplification and Approximation for Banking Exams

Why This Chapter Matters

This chapter is the front door to banking quant. It combines number types, divisibility, HCF-LCM, simplification, and shortcut arithmetic, so a weak foundation here slows down many later chapters.

Core Ideas

• Separate the number families clearly: natural numbers count upward from $1$, whole numbers add $0$, integers include negatives, and real numbers include both rational and irrational values.
• Treat $\text{HCF}$ as the common factor that survives in all numbers, and $\text{LCM}$ as the smallest shared multiple.
• For divisibility checks, use digit patterns instead of long division. For example, divisibility by $3$ or $9$ depends on the sum of digits.
• Divisibility by $11$ comes from alternate-digit sums, and some less common tests like divisibility by $19$ can still save time in exam-style elimination.
• Approximation questions reward controlled rounding. Round only enough to separate the answer choices.
• When operations mix fractions, percentages, powers, and roots, use the execution order before touching the arithmetic.
• Shortcut multiplication is useful only after the structure is recognised. Do not apply a trick to the wrong number pattern.

High-Value Formulas

How To Approach Questions

1. Classify the question first: exact simplification, divisibility, unit digit, factor logic, or approximation.
2. If the question is about HCF or LCM, move to prime factors early instead of experimenting with random multiples.
3. Convert percentages and mixed fractions into simple equivalent forms before multiplying.
4. Use bracket order and reduce early to keep numbers small.
5. For approximation, round the numbers that have the weakest impact on the final option gap.
6. If a multiplication shortcut applies, write the nearest base such as 10, 100, or 1000 before calculating.

Worked Examples

Example 1

Prompt: Find $25\%$ of $48$ plus $50\%$ of $120$.

Approach: Use the fast conversions $25\%=\frac{1}{4}$ and $50\%=\frac{1}{2}$. Then $\frac{1}{4}\times 48=12$ and $\frac{1}{2}\times 120=60$. The total is $72$.

Example 2

Prompt: Approximate $2959.85÷16.001-34.99$.

Approach: Round to nearby friendly numbers: $2960÷16-35$. That gives $185-35=150$.

Example 3

Prompt: Find $46\times 98$ quickly.

Approach: Write $98=100-2$. Then $46\times 98=46\times 100-46\times 2=4600-92=4508$.

Example 4

Prompt: Find $65^2$ without long multiplication.

Approach: For a number ending in $5$, square the leading part with its next integer. Here $6\times 7=42$, and the ending is always $25$. So $65^2=4225$.

Common Mistakes

• Mixing up irrational numbers with ordinary fractions or terminating decimals.
• Confusing HCF and LCM because both are asked in factorisation form.
• Rounding every number aggressively, even when one awkward decimal controls the answer.
• Ignoring BODMAS order and adding before dividing.
• Treating approximation as exact arithmetic instead of option elimination.

Quick Revision

Strong number-system work is a combination of classification, factor logic, clean operation order, and controlled shortcuts.