Arithmetic Quick Reference Cheat Sheet - IIM CAT 2026

1. CAT Exam Pattern & Weightage Analysis

Arithmetic forms the backbone of the Quantitative Aptitude (QA) section in the Indian Institutes of Management Common Admission Test (IIM CAT). Historically, out of 22 questions in the QA section, Arithmetic accounts for 8 to 10 questions (approximately 35% to 45% weightage). Master fundamentals such as ratio proportions, percentages, indices, and basic number properties to secure high percentile scores in IIM CAT 2026.

2. Number Sets & Basic Properties

Understanding fundamental number classifications and their algebraic behavior is crucial for solving CAT-level quantitative problems efficiently.

Classification of Number Sets

• Natural Numbers (\(\mathbb{N}\)): \(\{1, 2, 3, 4, \dots\}\)
• Whole Numbers (\(\mathbb{W}\)): \(\{0, 1, 2, 3, \dots\}\)
• Integers (\(\mathbb{Z}\)): \(\{\dots, -2, -1, 0, 1, 2, \dots\}\)
• Rational Numbers (\(\mathbb{Q}\)): \(\{\frac{a}{b} \mid a, b \in \mathbb{Z}, b eq 0\}\)
• Real Numbers (\(\mathbb{R}\)): Union of Rational and Irrational Numbers

Fundamental Algebraic Properties

For all real numbers \(a, b, c \in \mathbb{R}\):

• Commutative Property: \(a+b = b+a\) and \(ab = ba\)
• Associative Property: \((a+b)+c = a+(b+c)\)
• Distributive Property: \(a(b + c) = ab + ac\)
• Identity Property: Additive identity is 0 (\(a + 0 = a\)); Multiplicative identity is 1 (\(a \cdot 1 = a\))
• Inverse Property: Additive inverse is \(-a\) (\(a + (-a) = 0\)); Multiplicative inverse is \(\frac{1}{a}\) for \(a eq 0\) (\(a \cdot \frac{1}{a} = 1\))

3. Order of Operations & Fraction Rules

Precision in execution prevents silly mistakes in computational questions under timed exam constraints.

Order of Operations (PEMDAS / BODMAS)

1. P / B: Parentheses / Brackets
2. E / O: Exponents / Orders
3. M & D: Multiplication & Division (evaluated left to right)
4. A & S: Addition & Subtraction (evaluated left to right)

Fraction Operations

• Addition / Subtraction: \[\frac{a}{b} \pm \frac{c}{d} = \frac{ad \pm bc}{bd}\]
• Multiplication: \[\frac{a}{b} \cdot \frac{c}{d} = \frac{ac}{bd}\]
• Division: \[\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \cdot \frac{d}{c} = \frac{ad}{bc}\]
• Simplification: \[\frac{ka}{kb} = \frac{a}{b} \quad (k eq 0)\]

4. Laws of Exponents & Radical Rules

Exponents and radicals frequently appear in simplify-and-evaluate questions and indices-based equations.

Laws of Exponents

• Product Rule: \(a^m \cdot a^n = a^{m+n}\)
• Quotient Rule: \(\frac{a^m}{a^n} = a^{m-n}\)
• Power Rule: \((a^m)^n = a^{mn}\)
• Power of a Product: \((ab)^n = a^n b^n\)
• Zero Exponent: \(a^0 = 1\) (where \(a eq 0\))
• Negative Exponent: \(a^{-n} = \frac{1}{a^n}\)

Radical Rules

• Rational Exponent Representation: \[a^{m/n} = \sqrt[n]{a^m} = (\sqrt[n]{a})^m\]
• Product Inside Radical: \[\sqrt{ab} = \sqrt{a} \cdot \sqrt{b}\]
• Quotient Inside Radical: \[\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}\]

5. Percentages, Ratios & Rates

Percentages form the groundwork for profit-loss, simple and compound interest, mixtures, and data interpretation sets.

• Percentage Calculation: \[P\% \text{ of } X = X \times \frac{P}{100}\]
• Percentage Change: \[\text{\% Change} = \frac{\text{New Value} - \text{Old Value}}{\text{Old Value}} \times 100\]

6. Frequently Asked Questions (FAQ)