Number System Questions for SSC CGL: Attempt These 30 Quesitons

What Is the Number System in SSC Exams?

The Number System is a key part of the SSC CGL Quant section, covering basic number types, divisibility, HCF, LCM, remainders, place values, and numerical logic. Questions are generally concept-based and test both accuracy and speed.

SSC Number System: Key Concepts and Types of Questions?

The number system is an important part of the SSC CGL Quant section. It covers basic types of numbers, their properties, and how to solve related questions quickly and accurately. This topic is asked regularly in both Tier 1 and Tier 2 exams.

Key Concepts to Know

• Types of Numbers: Natural, whole, integers, prime, composite, rational, irrational, and co-prime.
• Place Value and Face Value: Understand how digits are positioned in a number.
• Divisibility Rules: Especially for 2, 3, 5, 7, 9, 11, and 13.
• HCF and LCM: Frequently used in word problems.
• Remainders and Modulus: Includes remainder-based questions and divisibility logic.
• Base Conversions: Binary, decimal, octal — mainly asked in Tier 2.
• Unit and Last Digit: Common in product or power-based questions.
• Factors and Multiples: Total number of factors, sum, and patterns.
• Even and Odd Numbers: Often part of logic-based questions.

Types of Questions Asked

• Find the HCF or LCM of two or more numbers
• Remainder when a number is divided by another
• Unit digit of a product or power
• Convert between number systems
• Identify prime, composite, or co-prime numbers
• Smallest or largest number satisfying given condition

Number System Questions for SSC CGL: Concept & Examples

The number system is one of the most frequently tested topics in the SSC CGL Quantitative Aptitude section. Questions typically assess your understanding of number types, divisibility, factorization, HCF and LCM, remainders, and patterns in digits.

Below are some key subtopics with solved examples that follow the format Google AI uses to display in AI Overviews and Featured Snippets:

1. Classification of Numbers

This includes identifying different types of numbers: natural, whole, integers, rational, irrational, real, prime, composite, and co-prime numbers.

Example:
Which of the following is an irrational number?
a) √16 b) √12 c) √9 d) √25

Solution:
√16 = 4 (rational)
√12 = 2√3 (irrational)
√9 = 3 (rational)
√25 = 5 (rational)
Correct Answer: b) √12

2. Divisibility Rules

These questions test whether a number is divisible by another number without performing full division.

Example:
What is the value of K such that 72K460K is divisible by 6?
a) 4 b) 9 c) 7 d) 8

Solution:
Divisible by 2: Last digit (K) must be even.
Divisible by 3: Sum of digits = 7 + 2 + K + 4 + 6 + 0 + K = 19 + 2K
Try K = 4 → sum = 19 + 8 = 27 (divisible by 3), and 4 is even
Correct Answer: a) 4

3. LCM and HCF Problems

These involve direct calculation or real-life word problems using the relationship:
HCF × LCM = Product of the numbers

Example:
If HCF of two numbers is 11 and LCM is 693, and one number is 77, what is the other?

Solution:
Other number = (HCF × LCM) ÷ Given number = (11 × 693) ÷ 77 = 99

4. Remainders and Modular Arithmetic

These test your ability to work with remainders after division, often requiring logical deduction.

Example:
What is the remainder when 6799 is divided by 7?

Solution:
6799 ÷ 7 gives a remainder of 2

5. Unit Digit & Cyclicity

These involve finding the unit digit of large powers using digit cycles.

Example:
What is the unit digit of (2467)^153 + (342)^82?

Solution:
Last digit of 2467 = 7 → cyclicity = [7, 9, 3, 1] → 153 mod 4 = 1 → unit digit = 7
Last digit of 342 = 2 → cyclicity = [2, 4, 8, 6] → 82 mod 4 = 2 → unit digit = 4
Sum = 7 + 4 = 11 → Unit digit = 1

Tips to Prepare for Number System in SSC CGL

• Focus on concept clarity before memorizing shortcuts
• Revise all divisibility rules from 2 to 13
• Practice questions involving LCM, HCF, and remainders with different variations
• Create a cheat sheet of cyclic patterns for quick reference
• Solve previous year SSC papers and timed mock tests regularly
• Don’t skip binary and base system conversions (important in Tier 2)

Common Mistakes Made by Students in SSC CGL Number System Questions

Every year, many SSC CGL aspirants lose marks in the Number System section due to small but frequent errors. Below is a simple list of common mistakes that students should avoid while preparing and attempting these questions:

• Ignoring basic definitions and properties like types of numbers (natural, whole, integers, prime, co-prime) or place value concepts.
• Confusing HCF and LCM in word problems or using incorrect steps in their calculation.
• Using divisibility rules incorrectly or forgetting them completely, especially for numbers like 7, 11, and 13.
• Applying formulas blindly without checking if the given condition or number type fits (e.g. applying even number logic to odd numbers).
• Overcomplicating simple questions instead of identifying patterns or logic-based shortcuts.
• Misreading what is being asked especially in questions about remainders, units digit, or greatest/smallest number satisfying certain conditions.
• Not practicing questions on base conversions like binary, octal, or decimal often ignored but asked in exams.
• Making calculation errors in basic multiplication, subtraction, or division especially under time pressure.
• Avoiding word-based number system questions that require both mathematical understanding and logical thinking.
• Skipping revision of core topics in favor of Arithmetic or Algebra, leading to weak performance in Number System.

Also check SSC CGL Maths Syllabus

SSC CGL Number System Questions

Number System is a fundamental topic in SSC CGL Quant, and questions are usually concept-based but easy to solve with proper practice. Below are some important Number System questions that reflect the level and pattern commonly asked in SSC CGL exams.

Q1. The sum of three consecutive natural numbers each divisible by 3 is 72. What is the largest among them?
A) 27
B) 25
C) 30
D) 26
Correct Answer: A

Q2. How many numbers between 1000 and 5000 are exactly divisible by 225?
A) 12
B) 15
C) 18
D) 20
Correct Answer: B

Q3. Two numbers differ by 5. If their product is 336, the sum of the two numbers is:
A) 51
B) 37
C) 31
D) 26
Correct Answer: C

Q4. When a number is divided by 56, the remainder obtained is 29. What will be the remainder when the number is divided by 8?
A) 5
B) 3
C) 4
D) 7
Correct Answer: A

Q5. The digits of a two-digit number are in the ratio of 2:3 and the number obtained by interchanging the digits is bigger than the original number by 27. What is the original number?
A) 36
B) 48
C) 69
D) 98
Correct Answer: B

Q6. What is the smallest number that must be added to 1032 to make it divisible by 6?
A) 2
B) 3
C) 4
D) 5
Correct Answer: A

Q7. Find the least number which when divided by 12, 15, and 20 leaves a remainder of 3 in each case.
A) 243
B) 243
C) 243
D) 243
Correct Answer: A

Q8. If a number leaves a remainder 1 when divided by 3, 4, and 5, what is the least such number?
A) 61
B) 121
C) 61
D) 61
Correct Answer: A

Q9. The unit digit of the product 237 × 189 × 543 is:
A) 9
B) 3
C) 7
D) 1
Correct Answer: B

Q10. What is the greatest 3-digit number divisible by 24, 36, and 54?
A) 972
B) 984
C) 936
D) 888
Correct Answer: C

Q11. How many 3-digit numbers are divisible by 11?
A) 81
B) 82
C) 90
D) 91
Correct Answer: B

Q12. If 4A7 is divisible by 11, what is the value of A?
A) 4
B) 5
C) 6
D) 7
Correct Answer: C

Q13. A number when divided by 13 leaves a remainder of 5. What is the remainder when twice that number is divided by 13?
A) 10
B) 3
C) 11
D) 4
Correct Answer: C

Q14. Which one of the following is not a prime number?
A) 191
B) 223
C) 221
D) 211
Correct Answer: C

Q15. What is the smallest number that is exactly divisible by 6, 8, 12 and 15?
A) 120
B) 240
C) 360
D) 180
Correct Answer: C

Q16. If the difference between a number and its square is 132, find the number.
A) 12
B) 11
C) 10
D) 9
Correct Answer: A

Q17. The sum of digits of a number is 18 and the number is divisible by 9. Which of the following could be the number?
A) 126
B) 261
C) 153
D) 234
Correct Answer: C

Q18. What is the remainder when 4⁷ is divided by 5?
A) 1
B) 2
C) 3
D) 4
Correct Answer: A

Q19. A number has 3 digits. If the sum of its digits is 12 and it is divisible by 6, which of the following could be that number?
A) 258
B) 462
C) 624
D) 345
Correct Answer: A

Q20. What is the HCF of 96 and 404?
A) 4
B) 8
C) 12
D) 2
Correct Answer: B

Q21. What is the LCM of 18, 24, and 36?
A) 144
B) 72
C) 216
D) 108
Correct Answer: D

Q22. The product of two numbers is 1200. If their HCF is 10, what is their LCM?
A) 100
B) 120
C) 130
D) 120
Correct Answer: B

Q23. Which of the following is a co-prime pair?
A) 18 and 24
B) 12 and 35
C) 14 and 21
D) 15 and 30
Correct Answer: B

Q24. Find the smallest number which when divided by 5, 6 and 7 leaves a remainder 3 in each case.
A) 213
B) 219
C) 213
D) 219
Correct Answer: A

Q25. The sum of two consecutive odd numbers is 56. What are the numbers?
A) 27 and 29
B) 25 and 31
C) 29 and 31
D) 27 and 31
Correct Answer: C

Q26. If a number is divisible by both 2 and 3, then it must be divisible by:
A) 5
B) 6
C) 8
D) 9
Correct Answer: B

Q27. A number is divisible by 9 and ends in 2. Which of the following can be the number?
A) 162
B) 252
C) 342
D) None of these
Correct Answer: D

Q28. What will be the sum of digits of the smallest 3-digit number divisible by 19?
A) 9
B) 6
C) 4
D) 7
Correct Answer: B

Q29. What is the total number of factors of 120?
A) 14
B) 15
C) 16
D) 12
Correct Answer: C

Q30. Find the least number which when divided by 4, 6, and 9 leaves remainder 1 in each case.
A) 73
B) 109
C) 145
D) 181
Correct Answer: D

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Key Takeaways for SSC Number System Preparation

• The Number System is a high-frequency topic in SSC exams, especially in the Quant section of CGL, CHSL, and MTS.
• Important concepts include types of numbers, place value, HCF, LCM, remainders, unit digit, and base conversions.
• Divisibility rules and modular arithmetic are essential for solving questions quickly and accurately.
• Questions are usually straightforward but require clarity of concepts and strong calculation skills.
• Regular practice of previous year questions and mock tests helps build speed and confidence.
• Common mistakes include misapplying divisibility rules, confusing HCF with LCM, and calculation errors under time pressure.
• Understanding the logic behind each type of problem is more important than just memorizing formulas.
• This topic plays a key role in Tier 1 scoring and also appears in advanced form in Tier 2.

SSC CGL Number System – FAQs

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