Number System Questions For CAT: Important Topics, Sample Questions & Best Books

By Shubhra Anand Jain|Updated : April 20th, 2022

CAT Questions on Number System are important for the candidates to understand as these questions have been regularly asked in the Exam. Number System is an important topic in the CAT Quantitative Aptitude section and therefore, candidates must practice them so that they ace this topic. Number System Questions for CAT are generally asked to test the aspirant’s knowledge of the concepts of Factors, HCF & LCM, Remainders, Base Theorem, etc. 

As per the expert analysis, the candidates can expect 1-2 questions from the Number System Questions for CAT. The difficulty level of questions is generally moderate. The Number System section is a vast topic and consists of a number of tricks and formulas. In this article, you will get all the important details for CAT Questions on Number System.

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Number System CAT Questions - Topics

The Number System Questions for CAT consist of a large number of sub-topics such as LCM, HCF, Factorial, etc. The number of Questions on the Number System is quite less compared to the other topics in the Quantitative Aptitude section. The candidates need to practice them well to ace these questions accurately. 

Go through the detailed CAT Syllabus to understand the topics from which the majority of questions are asked. Given below is the list of topics included in the Number System Questions for CAT:

  • LCM & HCF
  • Divisibility Rules
  • Base Change
  • Finding Units Place and Tens Place of a Number
  • Cyclicity
  • Remainders
  • Prime Factorization
  • Factorials
  • Indices and Surds

The above-given topics of Number System CAT Questions if practiced thoroughly by the candidates can easily solve CAT Questions on Number System. CAT Exam authority does not release the official syllabus. The above-mentioned topics are curated by BYJU’S Exam Prep Expert, by analyzing the CAT Question Paper.

Practice Number System Questions for CAT 

The candidates must be aware of the CAT Questions on the Number System with all the details. In order to make the candidates acquainted with the type of Number System CAT Questions, we have provided some examples below.

Question 1: How many three-digit numbers are greater than 100 and increase by 198 when the three digits are arranged in the reverse order? 


Explanation: Let the numbers be of the form 100a+10b+c, where a, b, and c represent single digits. Then (100c+10b+a)-(100a+10b+c)=198 99c-99a=198 c-a = 2. Now, a can take the values 1-7. a cannot be zero as the initial number has 3 digits and cannot be 8 or 9 as then c would not be a single-digit number. Thus, there can be 7 cases. B can take the value of any digit from 0-9, as it does not affect the answer. Hence, the total cases will be 7*10=70.

Question 2: If ‘x’ is a whole number and ‘y’ is also a whole number. Then, (x + y)(x + y) is a

Answer: Whole Number

Explanation: Let us take x = 2 and y = 0

Then, (x + y)(x + y) = (2 + 0)(2 + 0) = 4

We can take multiple values and we will get that (x + y)(x + y) will be a whole number.

Question 3: P is a prime number and (p2 + 3) is also a prime number. The number of all such possible p’s is

Answer: 1 

Only one value of p can assume, which is 2 at P=2, P2 + 3 =7 which is also a prime number

while all other P’s are odd numbers, and hence their square is also an odd number. On adding 3, it will convert into an even number. But an even number except 2 is not a prime number.

P2 + 3 = an even number that can't be a prime number.

Question 4:a and b are irrational numbers such that a + b = q is a rational number, then a – b is

Answer: Always Irrational 


Given a and b are irrational numbers.

And, a + b = q

Then, we know that

a2 – b2 = (a + b)(a – b)

=a-b = (a2 b2)/(a=b) = (a2 - b2)/q

Above term will always be irrational

Number System Questions For CAT PDF

The candidates can download the PDF file for CAT Question on Number System to practice it in an offline mode. Click on the link below and download it to your device.

☛ Number System CAT Question Download PDF

How to Solve Number System CAT Questions?

The CAT Questions on Number System are considered an important topic and it is needed to be practiced well. To solve the problems of the number system, certain tips and tricks need to be followed. The candidates can follow the tips and tricks given below to solve Number System Questions for CAT.

  • The number system consists of a lot of concepts and formulas. If these are followed thoroughly the candidates will be able to solve the Number System CAT Question with ease.
  •  A lot of practice should be done to solve these questions in CAT Exam. 
  • Attempt BYJU’S Exam Prep Mock Tests to practice these questions in an exam-like environment.
  • Candidates should follow shortcut tips and tricks to solve Number System CAT Questions in an easy manner.

☛ Get detailed information about CAT Log Questions

Best Books for Number System Questions for CAT

In order to ace the Number System CAT Questions, candidates are advised to refer to the best study material for best preparation. 



Quantitative Aptitude For CAT


Quantitative Aptitude For CAT 

Arun Sharma

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  • The  Number System Questions for CAT are a common topic that can not be overlooked during the preparation. Generally, 1-2 questions can be expected from this topic. Candidates should practice well and must be well-versed with all the important topics for the CAT Questions on Number System.

  • The difficulty level of the quantitative aptitude section in the CAT 2022 exam was easy-moderate. However, Number System CAT Questions are generally of moderate difficulty level. Though, the difficulty level varies across all slots of the exam.

  • The topics included under the Number System Questions for CAT are given below:

    • LCM & HCF
    • Divisibility Rules
    • Base Change
    • Finding Units Place and Tens Place of a Number
    • Cyclicity
    • Remainders
    • Prime Factorization
    • Factorials
    • Indices and Surds
  • The number of CAT Questions on Number System is very less, but this chapter can not be neglected at all. The candidates should go through the basic concepts and formulas to solve these questions easily and accurately.

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