Number Systems for CAT 2025: Concepts, Shortcuts, and Solved Examples
One of the most scoring topics in the CAT exam is the number system. The foremost requirement to solve questions from this topic is to have clear conceptual clarity and logical skills.
Number System for CAT 2025 is by far the most scoring and the easiest topic to cover from the quantitative aptitude section in the CAT exam. To solve questions correctly from this section, you must have a very clear conceptual understanding of mathematics and delve proper logical skills. Moreover, this is the only topic where the direct use of shortcut tricks are recommended by experts and previous year toppers. To begin with we recommend that you focus on understanding what are the different types of numbers, next what is divisibility, HCF and LCM etc. This will ultimately help you to have a clear glance of what is important in this chapter.
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Important Topics from Number System CAT
You can check the vital topics here.
- HCF and LCM
- Factorization
- Numbers
- Factors
- Divisibility Rules
- Last Two Digits
- Base System
- Unit Digits
- Remainders
- Cyclicity
- Indices & Surds
Basic Concepts of Number System
You can go through the basics from the below table.
Basic Concepts | Explanation |
Types of Numbers |
|
Divisibility Rules |
|
HCF and LCM |
HCF X LCM = Product of Numbers |
Remainders & Modular Arithmetic |
R —> N ≡ r | M |
|
Cyclicity & Unit’s Digit |
|
Also Read:Common Executive MBA Application Questions and How to Answer Them
Formula Sheet Number System
Check the important formulas from this sheet.
Number System Formula Sheet -PDF Download |
Quick Check before CAT Exam
You can go through this check list before the exam.
Properties of Operations
Details | Particulars |
Cumulative Property of Addition | A + B = B + A |
Associative Property of Addition | (A + B) + C = A + (B + C) |
Cumulative Property of Multiplication | A x B = B x A |
Associative Property of Multiplication | (A x B) X C = A X (B x C) |
Distributive Property of Multiplication with respect to Addition | A x (B + C) = (A x B) + (A x C) |
Law of Indices
Particulars | Details |
anx an | am+n |
am/ an | am-nif m > n |
am/ an | 1 / an-mif m < n |
am/ an | a0= 1 if m = n |
(am)n | amn= (an)m |
Important Questions from Number System
Practice the following questions.
- If a 6-digit number is of the form 72A68B, and it is divisible by 88, find the value of A + B.
Ans = 12
- How many factors of 26 × 34 × 52are perfect squares?
Ans = 24
- Find the remainder when 798 is divided by 100
Ans = 49
- The product of two numbers is 10080, and their HCF is 48. Find the number of possible pairs of such numbers.
Ans = 0 pairs possible
- How many 3-digit numbers are divisible by 7 and have all digits distinct?
Ans = 100
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