Number System CAT Questions and Answers PDF Download

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.

• 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 25+ Number System CAT questions 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.

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• Each question includes answer choices and detailed solutions in the PDF to help you practice effectively.

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

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Important Number System CAT Questions with Solutions

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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Medium Level Number System CAT Questions 2025

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

Q2. What is the least number which, when divided by 9, 12, 15, leaves remainder 5 in each case?
a) 185
b) 185 + 5 = 190
c) 180
d) 185 + 3 = 188

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

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

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

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

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

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

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. 843 + 3 = 846
C. 843 + 1 = 844
D. 840

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

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

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

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

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Q12. If a=34×52a = 3^4 \times 5^2a=34×52 and b=32×53b = 3^2 \times 5^3b=32×53, find the HCF(a, b).

Options:
A. 32×523^2 \times 5^232×52
B. 34×533^4 \times 5^334×53
C. 32×513^2 \times 5^132×51
D. 33×523^3 \times 5^233×52

Q13. Find the number of positive divisors of 34×533^4 \times 5^334×53.

Options:
A. 15
B. 16
C. 20
D. 25

Q14. What is the remainder when 1110311^{103}11103 is divided by 10?

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

Click Here: Download CAT Arithmetic questions PDF with Solutions

Difficult Level Number System CAT Questions 2025

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

Q2. What is the sum of all positive integers less than 100 that are relatively prime to 100?
a) 3040
b) 3600
c) 3900
d) 4100

Q3. What is the remainder when 11^234 is divided by 13?
a) 1
b) 3
c) 11
d) 2

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

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

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

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

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

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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. 385385

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

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. 60

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Important Number System Formulas for CAT Exam 2025

1. Important Divisibility Rules

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

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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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Importance of Solving Number System CAT Questions for 2025

• Solving 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.

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Best Books for Number System Preparation for CAT Exam 2025

When preparing for the Number System CAT Questions 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, 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 with Solutions gives you an idea of the type and the difficulty level of the CAT exam

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