SSC GD CH 01

 # 1. CH 01 : NUMBER SYSTEM 

🔢 1. Types of Numbers

Type	Examples	Description
Natural Numbers	1, 2, 3, 4, 5…	Counting numbers starting from 1
Whole Numbers	0, 1, 2, 3…	Natural numbers + 0
Integers	…–3, –2, –1, 0, 1…	Positive & negative whole numbers
Rational Numbers	1/2, –3/4, 5	Can be written in form p/q, q ≠ 0
Irrational Numbers	√2, √3, π	Cannot be written as p/q; non-terminating
Real Numbers	All rational & irrational	Includes all the above

🧮 2. Even and Odd Numbers

• Even Numbers: Divisible by 2 → 2, 4, 6, 8…

• Odd Numbers: Not divisible by 2 → 1, 3, 5, 7…

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🔢 3. Prime and Composite Numbers

• Prime Numbers: Only 2 factors → 2, 3, 5, 7…

• Composite Numbers: More than 2 factors → 4, 6, 8, 9…

• Important: 2 is the only even prime number

• 1 is neither prime nor composite

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🔄 4. LCM and HCF

• LCM (Lowest Common Multiple):
  Smallest number divisible by all given numbers

• HCF (Highest Common Factor):
  Largest number that divides all given numbers

🔸 Example:

• LCM of 12 & 15 = 60

• HCF of 12 & 15 = 3

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📏 5. Divisibility Rules (Important for SSC GD)

Number	Divisibility Rule
2	Last digit is even (0, 2, 4, 6, 8)
3	Sum of digits divisible by 3
4	Last 2 digits divisible by 4
5	Last digit is 0 or 5
6	Divisible by both 2 and 3
8	Last 3 digits divisible by 8
9	Sum of digits divisible by 9
10	Ends with 0
11	(Sum of odd-position digits – even-position digits) divisible by 11

🔍 6. Place Value and Face Value

• Place Value: Value according to position
  → In 438, place value of 4 = 400

• Face Value: Actual digit itself
  → Face value of 4 = 4

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📉 7. Conversion of Numbers

• Fractions ↔ Decimals:
  1/2 = 0.5, 3/4 = 0.75

• Terminating Decimals: End after few digits (e.g., 0.25)

• Non-Terminating Decimals: Go on forever (e.g., 1/3 = 0.333…)

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🧠 SSC GD Tricks to Remember:

✅ Odd + Even = Odd
✅ Even + Even = Even
✅ Odd × Odd = Odd
✅ Even × Odd = Even

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📌 Important Points for SSC GD

• Memorize divisibility rules

• Practice LCM & HCF using prime factorization

• Solve at least 20–30 MCQs daily from Number System

• Focus on speed + accuracy 

🔹 Section A: Types of Numbers (1–15)

1. Which is the smallest natural number?
   a) 0 b) 1 c) –1 d) 2
   ➤ Ans: b) 1

2. Which is the smallest whole number?
   a) 0 b) 1 c) –1 d) 2
   ➤ Ans: a) 0

3. Which is not a rational number?
   a) 1/2 b) √3 c) –5 d) 0
   ➤ Ans: b) √3 (Irrational)

4. Which of the following is an irrational number?
   a) √2 b) 3/4 c) 1.25 d) –7
   ➤ Ans: a) √2

5. Which number is both even and prime?
   ➤ Ans: 2

6. Which is neither prime nor composite?
   ➤ Ans: 1

7. What is the face value of 7 in 3746?
   ➤ Ans: 7

8. What is the place value of 6 in 5621?
   ➤ Ans: 600

9. Is 0 a rational number?
   ➤ Ans: Yes

10. What type of number is π?
    ➤ Ans: Irrational

11. Which number is divisible by both 3 and 5?
    a) 15 b) 13 c) 18 d) 25
    ➤ Ans: a) 15

12. Sum of first 5 natural numbers?
    ➤ Ans: 1+2+3+4+5 = 15

13. Which of the following is not a whole number?
    a) 0 b) 5 c) –1 d) 9
    ➤ Ans: c) –1

14. Which of these numbers is prime?
    a) 4 b) 9 c) 11 d) 15
    ➤ Ans: c) 11

15. What is the product of two odd numbers?
    ➤ Ans: Odd

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🔹 Section B: LCM & HCF (16–30)

16. LCM of 12 and 18?
    ➤ Ans: 36

17. HCF of 12 and 18?
    ➤ Ans: 6

18. LCM of 5 and 20?
    ➤ Ans: 20

19. HCF of 45 and 75?
    ➤ Ans: 15

20. LCM of 8, 12, and 20?
    ➤ Ans: 120

21. HCF of 0 and 9?
    ➤ Ans: 9

22. What is the HCF of two prime numbers?
    ➤ Ans: 1

23. LCM of two co-prime numbers 4 and 9?
    ➤ Ans: 36

24. HCF of 16 and 64?
    ➤ Ans: 16

25. LCM of 6 and 14?
    ➤ Ans: 42

26. HCF of 10 and 25?
    ➤ Ans: 5

27. LCM of 3 and 7?
    ➤ Ans: 21

28. LCM and HCF of same number (e.g. 9, 9)?
    ➤ Ans: 9 (both)

29. If HCF = 1, numbers are called?
    ➤ Ans: Co-prime

30. LCM of 1 and any number = ?
    ➤ Ans: The number itself

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🔹 Section C: Divisibility Rules (31–50)

31. Number divisible by 2?
    ➤ Ans: Any number ending in 0, 2, 4, 6, 8

32. Number divisible by 3: 372?
    3+7+2 = 12 → 12 divisible by 3
    ➤ Ans: Yes

33. Divisible by 4: 816?
    Last two digits: 16 → divisible by 4
    ➤ Ans: Yes

34. Divisible by 5: 785?
    Ends in 5 → Yes

35. Divisible by 6: 246?
    Divisible by both 2 and 3 → Yes

36. Divisible by 8: 512?
    Last 3 digits = 512 → 512 ÷ 8 = 64 → Yes

37. Divisible by 9: 153?
    Sum = 9 → Yes

38. Divisible by 10: 120?
    Ends in 0 → Yes

39. Divisible by 11: 121?
    1 – 2 + 1 = 0 → divisible by 11 → Yes

40. Number divisible by 3 and 4 is divisible by?
    ➤ Ans: 12

41. Which of these is divisible by 9: 729, 315, 222?
    ➤ Ans: 729

42. Divisible by 6: 144?
    144 ÷ 2 = 72; 144 ÷ 3 = 48 → Yes

43. A number divisible by 10 must end in:
    ➤ Ans: 0

44. If a number is divisible by 4 and 6, it is also divisible by?
    ➤ Ans: 12

45. Which of these is divisible by 8?
    a) 624 b) 254 c) 510 d) 333
    ➤ Ans: a) 624

46. Divisibility rule of 3: sum of digits = ?
    ➤ Ans: Should be divisible by 3

47. Divisibility rule of 11 involves?
    ➤ Ans: Alternating sum of digits

48. Which of the following is divisible by 4? 812, 225, 345
    ➤ Ans: 812

49. Which of these numbers is divisible by 5 but not by 10?
    ➤ Ans: Any number ending in 5

50. Number ends with 0, divisible by:
    ➤ Ans: 2, 5, 10

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🔹 Section D: Mixed Practice (51–70)

51. Convert 3/4 to decimal:
    ➤ Ans: 0.75

52. Is 0.333... a rational number?
    ➤ Ans: Yes (1/3)

53. Is √25 a rational number?
    ➤ Ans: Yes → 5

54. Sum of first 10 natural numbers?
    ➤ Ans: 55

55. Smallest 2-digit prime number?
    ➤ Ans: 11

56. Odd + Even = ?
    ➤ Ans: Odd

57. Even × Even = ?
    ➤ Ans: Even

58. Odd × Odd = ?
    ➤ Ans: Odd

59. Even + Even = ?
    ➤ Ans: Even

60. Is 121 a perfect square?
    ➤ Ans: Yes (11²)

61. Is √3 a rational number?
    ➤ Ans: No

62. What type of number is 1.333...?
    ➤ Ans: Rational (4/3)

63. Can irrational + rational = rational?
    ➤ Ans: No

64. Which is not a perfect square?
    a) 16 b) 81 c) 20 d) 49
    ➤ Ans: c) 20

65. Decimal of 1/2 = ?
    ➤ Ans: 0.5

66. Place value of 5 in 2593?
    ➤ Ans: 500

67. Face value of 7 in 374?
    ➤ Ans: 7

68. Product of two negative numbers?
    ➤ Ans: Positive

69. What is the reciprocal of 5/8?
    ➤ Ans: 8/5

70. A number divisible by 2 and 5 is also divisible by?
    ➤ Ans: 10

📄 Previous Year Number System Questions

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1. Greatest 5-digit number divisible by 5, 8, 15, 16 & 21

Q: What is the largest five-digit number that is divisible by 5, 8, 15, 16, and 21?

• Solution:
  Calculate LCM of 5, 8, 15, 16, 21 → 1680.
  Largest 5-digit = 99999; divide by 1680: remainder 1175 → subtract → 99120. 

• Answer: 99120

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2. Remainder when $2^{24}-1$ is divided by 7

Q: When $2^{24} - 1$ is divided by 7, what is the remainder?

• Solution:
  $2^3 \equiv 1 \mod 7$, so $2^{24} = (2^3)^8 \equiv 1^8 = 1$.
  $2^{24} -1 ≡ 0 \mod 7$. 

• Answer: 0

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3. Missing digits in divisibility by 3, 7 & 11

Q: The number 672xy is divisible by 3, 7, and 11. What is the value of $6x + 5y$?

• Solution:
  Trial gives x = 2, y = 1.
  Then $6×2 + 5×1 = 12 + 5 = 17$. 

• Answer: 17

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4. Divisibility by 72 (8 × 9)

Q: In the number 489x6378y, which is divisible by 72, find $\sqrt{8x + 6y}$.

• Solution:
  For divisibility by 8 and 9 → x = 5, y = 4.
  Compute: $\sqrt{8×5 + 6×4} = \sqrt{64} = 8$. 

• Answer: 8

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5. Divisor is 18×Quotient and 9×Remainder

Q: In a division, divisor = 18×quotient = 9×remainder. If remainder is 26, find dividend.

• Answer choices include: 3055, 3072, 3068, 3042

• Solution:
  Let quotient = q. Then divisor = 18q; remainder = 26 = divisor/9 = 2q → q = 13 → divisor = 234.
  Dividend = divisor×quotient + remainder = 234×13 + 26 = 3042 + 26 = 3068. 

• Answer: 3068

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6. Sum & difference to find product

Q: The sum of two numbers is 14 and their difference is 4. What is their product?

• Solution:
  Let numbers = 9 and 5 (half-sum ± half-diff).
  Product = 9 × 5 = 45.

• Answer: 45

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7. Largest six-digit divisible by multiple numbers

Q: Find the greatest six-digit number divisible by 42, 44, 26, 39 & 40.

• Answer options: 960954, 960960, 960945, 960958

• Solution:
  LCM of all = 27720; dividing 999999 gives quotient 36, remainder 2079 → 999999 – remainder = 960960. 

• Answer: 960960

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✅ Want More?

• You can download the full SSC/Maths Number System previous-year questions and solutions from SSC STUDY site — includes many such problems 

• Or I can create a PDF compilation of these problems for quick revision.