# CAT Number System Syllabus and Preparation Tips

CAT Number System Syllabus and Preparation Tips? The number system is a crucial topic in the CAT quantitative aptitude section. It serves as the foundation for other areas such as algebra, arithmetic, and modern maths. Although the number system questions have declined in recent CAT exams, it is still important to prepare for this topic.

## The syllabus for the number system can be categorized into the following subtopics:

1. Properties of numbers
2. Divisibility rules
3. Factorization
4. Concepts of HCF and LCM
5. Concepts of finding remainders
6. Unit digits and last two digits
7. Factorial based problems
8. Base system

According to a bar graph showing the percentages of questions from the number system in CAT exams between 2000 to 2008, more than 50% of the questions are from the properties of numbers.

## To prepare for the CAT number system, it is important to focus on the fundamental concepts within each subtopic. These include:

1. Properties of numbers: Understand the properties of prime numbers, co-prime numbers, perfect squares, decimals, and fractions. Pay special attention to prime numbers greater than 3, which can be written in the form of 6k + 1 or 6k-1.

2. Divisibility rules: Learn the divisibility rules of numbers from 2 to 13. In cases where the number is greater than 13, factorize it into smaller numbers and apply the divisibility rules of its factors.

3. Factorization: Master the prime factorization of three-digit or four-digit composite numbers. Practice problems related to HCF, LCM, integral solutions, and splitting numbers.

4. HCF and LCM: Understand the concepts of HCF and LCM and their applications in various types of questions. Develop a quick method for finding the LCM of multiple numbers.

5. Remainders: Focus on solving remainder questions based on the basics of remainders. Familiarize yourself with Euler theorem and Fermat theorem for more complex remainder problems.

6. Unit digit and last two digits: Use the concept of cyclicity to determine the unit digit of a number. Practice finding the last two digits of a number using methods such as binomial expansion.

7. Factorials and Base system: If you are short on time or find these topics challenging, you can prioritize other subtopics. However, practice problems related to trailing zeros, prime exponents in factorials, and conversion between decimal and other number bases.

In terms of preparation strategy, start by understanding the properties of numbers and then gradually move on to other subtopics as listed above. Solve simple problems first and then progress to more advanced questions that require multiple concepts or properties. Practice with past year CAT questions to get a sense of the difficulty level that helps you to understand the CAT Number System Syllabus and Preparation tips. It is also recommended to go through the derivation of critical formulas and concepts whenever possible. This will deepen your understanding and allow you to manipulate the concepts if variations arise in the questions.

Take topic-wise tests to assess your competency and build confidence. This will help you apply the concepts and handle different question variations.

Overall, thorough preparation of the number system is essential for performing well in the CAT quantitative aptitude section.

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