50+ Number System CAT Questions and Answers PDF Download

Q: What types of number system questions are asked in the CAT exam?

The CAT exam generally includes questions from topics such as divisibility rules, factors and multiples, LCM and HCF, prime numbers, number properties, remainders, base systems, and cyclicity.

Q: How important is the number system topic for CAT Quantitative Aptitude?

The number system is a fundamental topic and frequently appears in the CAT Quantitative Aptitude section. A good grasp of this concept can significantly improve your problem-solving speed and accuracy.

Q: Can number system CAT questions be solved without using complex formulas?

Yes, many number system questions in CAT rely on logical reasoning and fundamental properties of numbers, rather than complex formulas. Understanding concepts thoroughly is key

Q: What is the best strategy to prepare for number system questions for CAT?

Focus on conceptual clarity, practice a variety of problems, and revise topics like remainders, divisibility, and number properties. Solving previous year CAT papers and mock tests also helps reinforce understanding.

Author : Lalita Vishwakarma

November 26, 2025

Overview: Number System is a high-scoring topic of the Quantitative Ability (QA) section of the CAT exam. To ace this section, you need to practice some important Number System CAT questions 2026

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 the CAT exam, ranging from easy to difficult levels.
This will help you to improve the speed and accuracy of the section.

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 mathematical problems in the CAT exam that assess understanding of number properties and arithmetic operations.

They cover topics like types of numbers (Natural, Integers, Rational), divisibility rules, and prime numbers.
Concepts such as HCF, LCM, remainders, and modular arithmetic are frequently tested.
These questions are foundational in the Quant section and often appear in easy to moderate difficulty.
Mastery of number system questions for CAT helps improve speed and accuracy in solving quantitative problems.

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

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

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

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

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Medium Level CAT Number System Questions 2026

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

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

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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

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

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

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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

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

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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.

Important Number System Formulas for CAT Exam 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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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:

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

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.
These questions often test basic concepts like divisibility, factors, and remainders.
With practice, they can be solved quickly, helping save time in the exam.
They also enhance logical thinking and analytical skills.
Strong command over this topic boosts overall CAT Quant performance.

Best Books for Number System Preparation for CAT Exam 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 range from easy to difficult, allowing students to practice their skills at different levels.

By working through these problems, you can build a strong understanding of number system concepts, improve your problem-solving abilities, and boost your confidence for the exam.

Overall, this set of CAT Number System Questions pdf Number System CAT Questions with Solutions gives you an idea of the type and the difficulty level of the CAT exam

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