Arithmetic Formula Sheet & Concept Guide - IIM CAT 2026

Comprehensive LibreTexts-style chapter-wise study material and reference sheet for Quantitative Aptitude (Arithmetic) targeting IIM CAT 2026. Includes core definitions, fundamental properties, formulas, and analysis of NTA/IIM exam patterns.

Table of Contents

• 1. Number Systems & Properties
• 2. Percentages, Profit & Loss
• 3. Simple & Compound Interest
• 4. CAT Exam Pattern & Weightage Analysis
• 5. Frequently Asked Questions (FAQ)

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1. Number Systems & Properties

Number systems form the foundation of quantitative aptitude in competitive exams like CAT 2026. Understanding the classifications and operational properties is essential for solving complex arithmetic problems efficiently.

Types of Numbers

• Natural Numbers (\(\mathbb{N}\)): The counting numbers starting from 1: \(\{1, 2, 3, \dots\}\).
• Whole Numbers (\(\mathbb{W}\)): Natural numbers along with zero: \(\{0, 1, 2, 3, \dots\}\).
• Integers (\(\mathbb{Z}\)): All positive and negative whole numbers including zero: \(\{\dots, -2, -1, 0, 1, 2, \dots\}\).
• Rational Numbers (\(\mathbb{Q}\)): Numbers that can be expressed as a fraction \(\frac{a}{b}\), where \(a, b \in \mathbb{Z}\) and \(b eq 0\).

Fundamental Algebraic Properties

• Commutative Property: \(a+b = b+a\) and \(a \cdot b = b \cdot a\)
• Associative Property: \((a+b)+c = a+(b+c)\) and \((a \cdot b) \cdot c = a \cdot (b \cdot c)\)
• Distributive Property: \(a \cdot (b + c) = a \cdot b + a \cdot c\)

HCF & LCM Properties

Highest Common Factor (HCF) and Least Common Multiple (LCM) applications regularly appear in CAT questions involving time, work, and periodic cycles.

\[ \text{HCF}(a, b) \times \text{LCM}(a, b) = a \times b \]\[ \text{HCF of Fractions} = \frac{\text{HCF of Numerators}}{\text{LCM of Denominators}} \]\[ \text{LCM of Fractions} = \frac{\text{LCM of Numerators}}{\text{HCF of Denominators}} "]

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2. Percentages, Profit & Loss

Percentages serve as the core backbone of the entire Arithmetic module in CAT. Mastering fractional equivalents and percentage variations accelerates problem-solving speed drastically.

Percentage Formulas

\[ \text{Percentage} = ( \frac{\text{Value}}{\text{Total Value}} ) \times 100 \]\[ \% \text{ Change} = \frac{\text{New Value} - \text{Old Value}}{\text{Old Value}} \times 100 \]

Profit, Loss & Discount

Commercial arithmetic focuses on cost price (CP), selling price (SP), and marked price (MP).

\[ \text{Profit (P)} = \text{SP} - \text{CP}, \quad \text{Loss (L)} = \text{CP} - \text{SP} \]\[ \text{Profit \%} = (\frac{\text{Profit}}{\text{CP}}) \times 100, \quad \text{Loss \%} = (\frac{\text{Loss}}{\text{CP}}) \times 100 \]\[ \text{Discount} = \text{MP} - \text{SP} \]\[ \text{Discount \%} = (\frac{\text{Discount}}{\text{MP}}) \times 100 "]

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3. Simple & Compound Interest

Interest calculations measure the time value of money, contrasting linear growth (Simple Interest) with exponential growth (Compound Interest).

Simple Interest (SI) Formulas

\[ \text{SI} = \frac{P \times R \times T}{100} \]\[ \text{Amount (A)} = P + \text{SI} = P \cdot (1 + \frac{R \times T}{100}) \]

• \(P\) = Principal Amount
• \(R\) = Rate of Interest per annum (%)
• \(T\) = Time duration in years

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4. CAT Exam Pattern & Weightage Analysis

In recent IIM CAT examinations, Arithmetic accounts for approximately 35% to 45% of the total Quantitative Aptitude (QA) section. Analyzing previous years' questions (PYQs) reveals key insights into topic distribution:

• Chapter Weightage: Percentages, Profit & Loss, and Ratio & Proportion consistently contribute 4-6 questions per slot.
• NTA & CAT Pattern Trends: Questions blend multiple arithmetic concepts—such as combining weighted averages with percentage growth or interest compounding with ratios.
• PYQ Analysis: Regular practice with over 10,000+ past exam questions builds speed and sharpens elimination strategies for tricky TITA (Type In The Answer) questions.

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5. Frequently Asked Questions (People Also Ask)

What is the weightage of Arithmetic in IIM CAT Quantitative Aptitude?

Arithmetic typically constitutes the largest individual section in QA, representing roughly 8 to 10 questions out of 22 in recent CAT formats.

Are basic properties like Commutative and Distributive laws directly tested in CAT 2026?

While direct definition questions are rare, these fundamental properties form the operational basis for simplifying complex algebraic and numerical expressions under timed conditions.

How do I calculate the HCF and LCM of fractions quickly?

To find the HCF of fractions, calculate the HCF of the numerators and divide by the LCM of the denominators. Conversely, for the LCM of fractions, calculate the LCM of the numerators and divide by the HCF of the denominators.