Important Number System Questions for SSC Exams, Practice Here

Number System is a very important topic in exams like SSC CGL, CHSL, Banking, Railways, and Insurance. These questions check your basic maths skills and speed. In this blog, we have given important Number System questions that are often asked in these exams. Practice these questions to improve your preparation and do well in your upcoming exams.

What Are the Common Mistakes Students Make While Attempting Number System Questions?

While solving number system questions in competitive exams, students often make mistakes due to haste or lack of clarity in basic concepts. Common errors include:

• Misreading the question – ignoring key words like “smallest,” “greatest,” “remainder,” or “divisible” can lead to choosing the wrong method or option.
• Calculation mistakes – especially in multiplication, squaring, or when dealing with large numbers or decimals.
• Skipping steps – trying to mentally solve complex logic without writing it down leads to confusion.
• Not applying shortcuts or divisibility rules forgetting tricks like LCM-HCF relations or digital root tricks causes time loss.
• Lack of time management – spending too long on one tough question instead of moving on.
• Not revising formulas – being unclear about formulas like Product=LCM×HCF Product = LCM × HCF Product=LCM×HCF or misusing place value logic in digit problems.

Tips and Tricks to Solve Number System Questions Quickly

To score well in the number system section of government exams like SSC exams, Banking, Railways, and Insurance, it’s important to learn shortcuts and smart solving methods. Here are some useful tips and tricks:

• Understand Number Properties: Learn types of numbers – natural, whole, even, odd, prime, composite – and how they behave in operations.
• Use Divisibility Rules: Memorize rules for 2, 3, 4, 5, 6, 8, 9, and 11 to save time in checking if a number is divisible.
• Remember LCM and HCF Tricks:
  • LCM×HCF=Product of two numbers
  • Use prime factorization for fast results.
• Digit-Based Problems:
  • Use place value rules: if number is 10x + y, reversed = 10y + x.
  • Use basic algebra for sum or difference of digits.
• Learn Cyclicity of Units Digit: For units digit of large powers (e.g., 2^10), know the last digit patterns:
  • 2 → 2, 4, 8, 6 (repeats every 4)
• For Remainder Problems: Use
  • Chinese Remainder Theorem for complex cases
  • Try using the formula: Number=LCM×k±R
• Practice Approximation: For large numbers, estimate to nearest base like 10, 100, or round to simplify.
• Memorize Squares and Cubes: At least till 30 for fast spotting of perfect squares or cubes.
• Break the Problem Down: Don’t try to solve everything mentally; break it into smaller steps to avoid errors.
• Take Mock Tests: Regular practice with time limits improves both speed and accuracy.

Practice Questions for Number System

Here are 30 important Number System questions selected as per the latest exam trends. Practice them to improve your accuracy and boost your exam score.

Q1. The digits of a two-digit number are in the ratio 2:3. If the digits are interchanged, the new number is 27 more than the original. What is the original number?
A) 42
B) 69
C) 63
D) 84
Correct Answer: B) 69

Q2. A two-digit number is such that the sum of its digits is 11. If the digits are reversed, the new number is 9 more than the original. What is the original number?
A) 56
B) 65
C) 38
D) 47
Correct Answer: A) 56

Q3. The product of a number and its square is 306. What is the number?
A) 16
B) 18
C) 17
D) 19
Correct Answer: C) 17

Q4. What least number should be added to 1298 to make it divisible by 7?
A) 3
B) 4
C) 5
D) 2
Correct Answer: B) 4

Q5. A number leaves remainder 5 when divided by 8. What is the remainder when the same number is divided by 4?
A) 1
B) 2
C) 3
D) 0
Correct Answer: A) 1

Q6. The LCM of two numbers is 180, HCF is 6, and one number is 30. What is the other number?
A) 36
B) 42
C) 60
D) 48
Correct Answer: A) 36

Q7. How many numbers between 100 and 200 are divisible by both 3 and 4?
A) 6
B) 8
C) 10
D) 12
Correct Answer: B) 8

Q8. What is the least number that must be subtracted from 9400 to make it divisible by 23?
A) 4
B) 6
C) 10
D) 8
Correct Answer: D) 8

Q9. Find the greatest 4-digit number divisible by 15, 20, and 28.
A) 9960
B) 9840
C) 9990
D) 9660
Correct Answer: D) 9660

Q10. What is the HCF of 45, 75, and 120?
A) 30
B) 15
C) 10
D) 5
Correct Answer: B) 15

Q11. What is the LCM of 14, 18, and 22?
A) 1386
B) 1260
C) 1320
D) 1440
Correct Answer: A) 1386

Q12. The product of two consecutive natural numbers is 506. What are the numbers?
A) 20, 21
B) 21, 22
C) 22, 23
D) 23, 24
Correct Answer: C) 22, 23

Q13. Find the unit digit of the product of the first 10 odd natural numbers.
A) 5
B) 2
C) 0
D) 1
Correct Answer: C) 0

Q14. What is the least number which when added to 659 makes it a perfect square?
A) 2
B) 5
C) 17
D) 9
Correct Answer: C) 17

Q15. A number when divided by 5, 6, and 7 leaves a remainder 4 in each case. What is the smallest such number?
A) 214
B) 344
C) 298
D) 313
Correct Answer: A) 214

Q16. What is the least number which when divided by 8, 12, and 18 leaves a remainder of 3?
A) 75
B) 147
C) 183
D) 159
Correct Answer: B) 147

Q17. The sum of two numbers is 72 and their HCF is 6. How many such unique pairs exist?
A) 4
B) 5
C) 6
D) 7
Correct Answer: C) 6

Q18. If 2¹⁰ is divided by 7, what is the remainder?
A) 2
B) 4
C) 5
D) 3
Correct Answer: A) 2

Q19. Which of the following is divisible by 3 but not by 9?
A) 117
B) 234
C) 999
D) None of these
Correct Answer: D) None of these

Q20. What is the LCM of two numbers if their HCF is 8 and product is 960?
A) 120
B) 140
C) 100
D) 160
Correct Answer: A) 120

Q21. The number 3A7 is divisible by 11. What is the digit A?
A) 3
B) 6
C) 4
D) None of these
Correct Answer: D) None of these

Q22. The difference between the squares of two consecutive even numbers is 68. What are the numbers?
A) 14 and 16
B) 12 and 14
C) 18 and 20
D) 16 and 18
Correct Answer: D) 16 and 18

Q23. What is the smallest number which when increased by 17 is divisible by 20, 25, and 30?
A) 5817
B) 5983
C) 5880
D) 5940
Correct Answer: B) 5983

Q24. How many prime numbers are there between 10 and 50?
A) 9
B) 10
C) 11
D) 12
Correct Answer: C) 11

Q25. A number when divided by 4 gives a remainder of 3. Which of the following numbers is definitely not divisible by 4?
A) 23
B) 35
C) 47
D) All of these
Correct Answer: D) All of these

Q26. What is the sum of all two-digit numbers divisible by 9?
A) 585
B) 594
C) 576
D) 567
Correct Answer: A) 585

Q27. The HCF and LCM of two numbers are 8 and 480 respectively. If one number is 60, what is the other number?
A) 64
B) 96
C) 72
D) 80
Correct Answer: B) 96

Q28. Which is the smallest number which when divided by 9 and 10 leaves remainder 2?
A) 92
B) 112
C) 182
D) 272
Correct Answer: A) 92

Q29. Find the smallest 4-digit number divisible by 36.
A) 1008
B) 1000
C) 1032
D) 1044
Correct Answer: A) 1008

Q30. The sum of digits of a number is 9 and the number is divisible by 9. Which of the following could be the number?
A) 81
B) 72
C) 90
D) All of these
Correct Answer: D) All of these

Also attempt SSC CGL Practice Quiz

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