Course Content
Number System
This module focuses on Number System concepts through authentic CAT Previous Year Questions (PYQs), helping students build a strong foundation in one of the most frequently tested areas of Quantitative Aptitude. Learners will understand the behavior of numbers, identify common CAT traps, and apply concepts efficiently under exam conditions. The module covers core topics such as properties of numbers, divisibility, factors and multiples, LCM & HCF, remainders, base system, and cyclicity, all mapped directly to CAT PYQs from the last 15 years. Questions are arranged from easy to difficult, enabling a gradual increase in conceptual depth and problem-solving confidence. Special emphasis is given to pattern recognition, shortcut logic, and elimination techniques, which are crucial for saving time in the CAT exam. By the end of this module, students will be able to quickly assess number-based questions, decide whether to attempt or skip, and solve them with greater accuracy and speed.
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Properties of Numbers
Properties of Number
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Divisibility Divisibility – Core Concept
Divisibility-Core Concept
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Divisibility
1️⃣ Divisibility – Core Concept A number A is divisible by B if division of A by B leaves remainder 0. 🔹 CAT Insight: Divisibility is often tested indirectly through conditions, options elimination, or constraints, not direct rule-based questions. 2️⃣ Important Divisibility Rules (CAT-Relevant) Divisible by 2 Last digit is even (0, 2, 4, 6, 8) Divisible by 3 Sum of digits divisible by 3 Divisible by 4 Last two digits divisible by 4 Divisible by 5 Last digit is 0 or 5 Divisible by 6 Divisible by both 2 and 3 Divisible by 9 Sum of digits divisible by 9 Divisible by 11 Difference of sum of digits in alternate positions is 0 or a multiple of 11
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Percentage
Percentage
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CAT Quant PYQs (2023-2025)- 3 years: Complete Practice Course

📘 Properties of Numbers (CAT Quant)

The Properties of Numbers form the foundation of the Number System and are frequently tested in CAT through logic-based, remainder-based, and divisibility-based questions. CAT rarely asks direct formula questions; instead, it checks conceptual clarity and pattern recognition.

1️⃣ Classification of Numbers

Natural Numbers

Positive counting numbers: 1, 2, 3, …

Whole Numbers

0 and all natural numbers.

Integers

…, −3, −2, −1, 0, 1, 2, 3, …

Rational Numbers

Numbers that can be expressed as p/q, where q ≠ 0.

Irrational Numbers

Numbers that cannot be expressed as a fraction (e.g., √2, π).

🔹 CAT Focus: Identifying the type of number involved to apply the correct logic.

2️⃣ Even and Odd Numbers

  • Even number: Divisible by 2

  • Odd number: Not divisible by 2

Key Properties:

  • Even ± Even = Even

  • Odd ± Odd = Even

  • Even ± Odd = Odd

  • Even × Any = Even

  • Odd × Odd = Odd

🔹 CAT Application:
Used in parity-based elimination, especially in TITA questions.

3️⃣ Prime and Composite Numbers

Prime Number

A number greater than 1 with exactly two factors: 1 and itself.

Composite Number

A number with more than two factors.

Important Points:

  • 2 is the only even prime number

  • 1 is neither prime nor composite

🔹 CAT Focus:
Questions involving factor count, divisibility, and LCM–HCF logic.

4️⃣ Divisibility Rules (Conceptual Use)

Some commonly used divisibility checks:

  • Divisible by 2 → Last digit even

  • Divisible by 3 → Sum of digits divisible by 3

  • Divisible by 9 → Sum of digits divisible by 9

  • Divisible by 11 → Difference of alternating digit sums is 0 or a multiple of 11

🔹 CAT Tip:
Used for fast elimination, not lengthy calculations.

5️⃣ Factors and Multiples

Factor

A number that divides another number exactly.

Multiple

A number obtained by multiplying a given number by an integer.

Key Observations:

  • Every number has at least two factors: 1 and itself

  • Prime numbers have exactly two factors

  • Number of factors depends on prime factorization

🔹 CAT Focus:
Factor-based questions often combine remainder, divisibility, and LCM/HCF concepts.

6️⃣ Properties of Zero and One

Zero (0)

  • 0 multiplied by any number = 0

  • Division by 0 is undefined

One (1)

  • Multiplicative identity

  • Does not change the value when multiplied

🔹 CAT Trap:
Division involving zero and assumptions about factors of 1.

7️⃣ Positive and Negative Numbers

  • Product of two positive numbers → Positive

  • Product of two negative numbers → Positive

  • Product of positive and negative → Negative

🔹 CAT Use:
Sign-based logic in equations, inequalities, and remainder problems.

8️⃣ Absolute Value

Absolute value of a number is its distance from zero, always non-negative.

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