50+ Number System CAT Questions with Solutions (Free PDF Download)

Looking for Number System CAT Questions with Solutions? Here, you will find 50+ questions covering topics such as divisibility, remainders, HCF and LCM, factorials, prime numbers, and unit digits.

Every year, CAT Exam includes multiple Number System Questions either directly or indirectly in the Quantitative Aptitude section. These Number System CAT Questions test a candidate’s understanding of basic arithmetic, divisibility, factors, multiples, primes, remainders, and number properties.

The questions are divided into easy, medium, and difficult levels, so you can start with the basics and move to tougher ones. Detailed solutions are also provided to help you understand where you went wrong. You can also download the free PDF and practise whenever you want.

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CAT Number System Questions: Key Highlights

• The number system is one of the easiest sections of the quantitative aptitude section. Having a good hold on this section will help you achieve a high score in the exam.
• To help you out, we have provided 50+ CAT Number System questions PDF to match the difficulty of CAT exam, ranging from easy to difficult levels.
• This will help you to improve the speed and accuracy of the section.
• You can also practise CAT PYQs to get an idea of the types of Number System questions asked in the exam.
• Each question includes answer choices and detailed solutions in the PDF to help you practice effectively.

Scroll down CAT Number System Questions pdf with Solutions to practice them!

What are CAT Number System Questions?

Number System CAT Questions are based on basic properties of numbers and different arithmetic concepts. They are asked in the Quantitative Aptitude section and can be based on simple as well as mixed concepts.

• Questions can cover number types such as Natural Numbers, Integers, and Rational Numbers.
• Other common topics include divisibility rules, prime numbers, remainders, HCF, and LCM
• Some questions may also involve modular arithmetic and factors.
• Regular practice can help you solve Number System questions faster and improve your accuracy in the CAT Quant section.

Download Number System CAT Question and Answers PDF

CAT Number System Questions: Resources

CAT Number System Resources	Action
CAT Number System Questions	Download PDF
CAT Number System Mock Test	Attempt Now
CAT Number System Preparation Video	Watch Free Video

Important Number System CAT Questions 2026 with Solutions

Q1. What is the greatest 4-digit number exactly divisible by 88?
a) 9988
b) 9976
c) 9992
d) 9944

Correct Answer: d) 9944

Q2. If a number leaves a remainder 1 when divided by 2, 3 and 4, what is the smallest such number?
a) 10
b) 13
c) 25
d) 37

Correct Answer: b) 13

Important Links

Arithmetic Questions	Arithmetic Syllabus	Profit & Loss Questions
Averages Questions	Time & Work Questions	Time-Speed-Distance
Mixture & Alligation	CAT QA Questions	Calculate Percentage

Download Maths Mantra Formula Booklet by Supergrads

Q3. What is the sum of all 3-digit numbers divisible by 11?
a) 49455
b) 44550
c) 49815
d) 49700

Correct Answer: b) 44550

Check: How to prepare for Quantitative Aptitude for CAT exam

Q4. Find the units digit of 7⁷⁷⁷.
a) 1
b) 3
c) 7
d) 9

Correct Answer: c) 7

Q5. How many two-digit numbers are divisible by 7?
a) 11
b) 12
c) 13
d) 14

Correct Answer: c) 13

Download Number Theory Formula PDF by Supergrads

Q6. Find the unit digit of 71037^{103}7103

Options:
A. 3
B. 7
C. 9
D. 1

Correct Answer: C. 9

Check: How to prepare for Logical Reasoning for CAT 

Q7. What is the sum of first 50 even natural numbers?

Options:
A. 2550
B. 2600
C. 2400
D. 2450

Correct Answer: A. 2550

Q8. Which of the following is not a prime number?

Options:
A. 97
B. 89
C. 77
D. 83

Read More: How to Prepare for Data Interpretation for CAT Exam?

Correct Answer: C. 77

Q9. What is the sum of all single-digit prime numbers?

Options:
A. 15
B. 17
C. 18
D. 19

Correct Answer: B. 17

Q10. How many even numbers are there between 101 and 200 (both exclusive)?

Options:
A. 49
B. 50
C. 99
D. 100

Correct Answer: A. 49

Read More: Supergrads CAT Toppers Interview

How many Number System questions are asked in CAT QA?

Number System usually accounts for around 1 to 3 questions in the CAT Quantitative Aptitude section. The exact number can change from year to year. In some papers, questions are directly based on Number System, while some may combine its concepts with Arithmetic or Algebra. It is an important part of the CAT Syllabus to cover during preparation.

What are the most important Number System topics for CAT (remainders, divisibility, HCF/LCM, factorials)?

The highest-priority Number System topics for CAT are remainders, divisibility rules, HCF & LCM, factors and multiples, factorials, cyclicity of powers, unit digit, base systems, and prime numbers. These concepts are frequently used to test logic, speed, and mathematical reasoning.

Medium Level CAT 2026 Number System Questions

Q1. A number when divided by 5 leaves remainder 4. What is the remainder when the square of the number is divided by 5?
a) 1
b) 4
c) 0
d) 3

Correct Answer: a) 1

Q2. What is the least number which, when divided by 9, 12, 15, leaves remainder 5 in each case?
a) 185
b)190
c) 180
d)  188

Correct Answer: a) 185

Download Complete Study Plan for QA by Supergrads

Q3. How many integers between 1 and 1000 are divisible by neither 2 nor 5?
a) 400
b) 300
c) 200
d) 100

Correct Answer: a) 400

Q4. How many trailing zeroes are there in 100!?
a) 20
b) 24
c) 22
d) 25

Correct Answer: b) 24

Know More | How Many Times CAT Exam is Conducted in a Year

Q5. What is the remainder when 17^23 is divided by 6?
a) 1
b) 5
c) 3
d) 2

Correct Answer: b) 5

Q6. What is the greatest 4-digit number which is exactly divisible by 15, 25, 40, and 75?

Options:

A. 9600
B. 9000
C. 10000
D. 9500

Correct Answer: A. 9600

Q7. What is the number of zeros at the end of 100!100!100!?

Options:
A. 24
B. 22
C. 25
D. 26

Correct Answer: A. 24

Q8. What is the smallest number that when divided by 5, 6, 7 and 8 leaves a remainder of 3 in each case?

Options:
A. 843
B. 846
C. 844
D. 840

Correct Answer: A. 843

Q9. The difference between the squares of two consecutive numbers is 65. What is the smaller number?

Options:
A. 32
B. 33
C. 64
D. 65

Correct Answer: A. 32

Download Number System Formula PDF by Supergrads

Q10. Find the greatest number that divides 12288 and 17496 exactly.

Options:
A. 24
B. 12
C. 72
D. 36

Correct Answer: A. 24

Q11. A number when divided by 8 leaves a remainder of 5. What will be the remainder when the same number is divided by 4?

Options:
A. 1
B. 2
C. 3
D. 0

Correct Answer: A. 1

Click Here: Download CAT Arithmetic questions PDF with Solutions

Are these Number System CAT questions based on previous year patterns?

Yes, most good CAT Number System question sets are designed using trends seen in previous CAT papers. They usually reflect the same difficulty level, logic style, and topic distribution that appears in actual exams.

Difficult Level Number System CAT Questions 2026

Q1. Find the number of divisors of 360.
a) 24
b) 30
c) 36
d) 32

Correct Answer: a) 24

Q2. What is the sum of all positive integers less than 100 that are relatively prime to 100?
a) 3040
b) 2000
c) 3900
d) 4100

Correct Answer: b) 2000

Q3. What is the remainder when 11^234 is divided by 13?
a) 1
b) 3
c) 11
d) 12

Correct Answer: d) 12

Q4. The product of two numbers is 2025 and their HCF is 15. Find the LCM.
a) 135
b) 225
c) 1350
d) 2025

Correct Answer: a) 135

Q5. What is the smallest 6-digit number divisible by 7, 9, and 11?
a) 100485
b) 100287
c) 100089
d) 100053

Correct Answer: a) 100485

Q6. Find the number of integers between 1 and 1000 (inclusive) that are not divisible by 2, 3 or 5.

Options:
A. 266
B. 267
C. 268
D. 270

Correct Answer: A. 266

Q7. How many 3-digit numbers are divisible by 9 but not by 3²?

Options:
A. 49
B. 0
C. 50
D. 99

Correct Answer: B. 0

Read More | CAT Mock Test Series

Q8. What is the sum of all 4-digit numbers divisible by 13?

Options:
A. 384384
B. 393993
C. 394394
D. 3810807

Correct Answer: D. 3810807

Download Arithmetic Formula PDF by Supergrads

Q9. How many positive integers less than 1000 are divisible by neither 2 nor 5?

Options:
A. 400
B. 300
C. 400.5
D. 399

Correct Answer: A. 400

Q10. Find the smallest number which, when divided by 3, 4, 5, and 6 leaves a remainder 2 in each case.

Options:
A. 122
B. 122 + 2 = 124
C. 118
D. 62

Correct Answer: D. 62

Also Check: CAT Total Marks and Weightage

Read More | Practice CAT Geometry Questions with Solutions

Why Are CAT Number System Questions Important?

Number System CAT Questions are essential for two reasons:

They help in building logical and analytical thinking, which is useful across Quant topics.

These questions are frequently asked in the CAT and related MBA entrance exams, making them high-yield.

Often appearing in moderate to difficult levels, Number System CAT Questions test the fundamental understanding of numbers, their properties, and patterns. Hence, early preparation and strategic revision of this topic are crucial for a competitive score.

What is the best way to practice Number System for CAT in 30 days?

If you have 30 days, divide your preparation into four weeks. Spend the first week clearing your basic concepts and formulas. In the second week, solve questions topic by topic. Use the third week for mixed question sets and timed practice. In the last week, revise the topics you find difficult and take a few mocks.

Try to practise every day and keep track of the questions you get wrong. Instead of just checking the answer, spend some time understanding your mistake and finding a quicker way to solve similar questions.

Important Number System Formulas for CAT 2026

1. Important Divisibility Rules

• By 2: Last digit is even.
• By 3: Sum of digits divisible by 3.
• By 4: Last 2 digits are divisible by 4.
• By 5: Last digit is 0 or 5.
• By 6: Divisible by both 2 and 3.
• By 8: Last 3 digits are divisible by 8.
• By 9: Sum of digits divisible by 9.
• By 11: Alternating sum of digits is divisible by 11.

Check: CAT Exam Pattern Latest Changes

2. HCF and LCM

• HCF × LCM = Product of two numbers
• For a=pm×qna = p^m \times q^na=pm×qn,
  Number of divisors = (m+1)(n+1)(m+1)(n+1)(m+1)(n+1)
• HCF = Lowest powers of common prime factors
• LCM = Highest powers of all prime factors

3. Basic Properties

• Even + Even = Even
• Even + Odd = Odd
• Odd + Odd = Even
• Even × Even = Even
• Odd × Odd = Odd

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Download Free Subject-wise CAT 2026 Syllabus PDF Now

Types of Number System CAT Questions Asked in Past Exams

Here are a few commonly observed formats of Number System CAT Questions in previous years:

1. Find the remainder when a large number is divided by a smaller number.
2. Identify how many factors a number has.
3. Determine the unit digit of a number raised to a high power.
4. Questions involving base conversions (binary, decimal).
5. Problems involving co-prime numbers and their properties

Why Number System CAT Questions Matter:

• Foundation of Quantitative Aptitude: Many topics in QA depend on Number System concepts.
• Frequent in Exams: Almost every CAT exam includes Number System CAT Questions.
• Scoring Potential: Once mastered, these questions are highly accurate and quick to solve.
• Concept Integration: Number System CAT Questions often combine with algebra and arithmetic.

Strong command over Number System CAT Questions can significantly improve your overall CAT score and boost confidence in the Quant section.

Importance of Solving Number System CAT Questions for 2026

• Solving CAT exam number system questions is vital as they frequently appear in the CAT exam.
• They form the foundation for many other Quant topics like Algebra and Arithmetic.
• Most of these questions cover basic concepts such as divisibility, factors, and remainders.
• With enough practice, you can solve many of them quickly and save valuable time during the exam.
• Regular practice also helps you improve your thinking and approach to different types of questions.
• A good understanding of Number System can help you perform better in the CAT Quant section.

Read More: Important CAT Para Jumble Questions with Answers

Best Books for Number System Preparation for CAT 2026

When preparing for the CAT Number System Questions PDF section of the CAT exam, it is important to refer to books that offer a structured approach to understanding the concepts, as well as practice questions to reinforce learning. Here are some of the best books for CAT Number System preparation:

Number System CAT Questions Books	Author	Publisher	Key Features	Best for
How to Prepare for Quantitative Aptitude for CAT	Arun Sharma	McGraw-Hill Education	Level-wise questions, a CAT-centric approach, detailed Number System chapter	All-level aspirants
Quantitative Aptitude for Competitive Examinations	R.S. Aggarwal	S. Chand Publishing	Strong fundamentals, variety of basic to moderate-level questions	Beginners and concept clarity seekers
Quantitative Aptitude Quantum CAT	Sarvesh K. Verma	Arihant Publications	Comprehensive theory, shortcut techniques, high-level CAT questions	Intermediate to advanced aspirants

Conclusion

These Number System CAT questions include easy, moderate, and difficult questions, so you can practise according to your current level.

Solving different types of questions will help you understand the concepts better and get more comfortable with the topic. It will also help you identify the areas where you need more practice.

CAT Number System Questions PDF includes questions with solutions and gives you an idea of the type of questions asked in the exam. You can use it for regular practice and revision to prepare better for the test and improve your CAT results.