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Number System questions

HCF, LCM, unit digits and remainders.

1. What is the remainder when 863 is divided by 14?

  1. 8
  2. 9
  3. 12
  4. 10
Answer

B. 9 863 = 14 × 61 + 9.

2. Three bells ring at intervals of 9, 20 and 6 minutes. If they ring together now, after how many minutes will they next ring together?

  1. 90 minutes
  2. 35 minutes
  3. 189 minutes
  4. 180 minutes
Answer

D. 180 minutes LCM(9, 20, 6) = 180 minutes.

3. What is the sum of the first 20 natural numbers?

  1. 400
  2. 210
  3. 420
  4. 190
Answer

B. 210 n(n + 1)/2 = 20 × 21/2 = 210.

4. Find the HCF of 99 and 44.

  1. 11
  2. 99
  3. 12
  4. 22
Answer

A. 11 99 = 11 × 9 and 44 = 11 × 4; 9 and 4 share no factor, so HCF = 11.

5. What is the unit digit of 3^54?

  1. 9
  2. 7
  3. 0
  4. 5
Answer

A. 9 Unit digits of 3^n repeat as 3, 9, 7, 1. 54 gives position 2 in the cycle, so 9.

6. What is the remainder when 260 is divided by 7?

  1. 1
  2. 6
  3. 2
  4. 3
Answer

A. 1 260 = 7 × 37 + 1.

7. Three bells ring at intervals of 9, 16 and 18 minutes. If they ring together now, after how many minutes will they next ring together?

  1. 144 minutes
  2. 288 minutes
  3. 43 minutes
  4. 72 minutes
Answer

A. 144 minutes LCM(9, 16, 18) = 144 minutes.

8. What is the sum of the first 12 natural numbers?

  1. 144
  2. 78
  3. 156
  4. 90
Answer

B. 78 n(n + 1)/2 = 12 × 13/2 = 78.

9. Find the HCF of 30 and 40.

  1. 30
  2. 9
  3. 10
  4. 11
Answer

C. 10 30 = 10 × 3 and 40 = 10 × 4; 3 and 4 share no factor, so HCF = 10.

10. What is the unit digit of 2^40?

  1. 8
  2. 6
  3. 4
  4. 2
Answer

B. 6 Unit digits of 2^n repeat as 2, 4, 8, 6. 40 gives position 4 in the cycle, so 6.

11. What is the remainder when 774 is divided by 11?

  1. 5
  2. 4
  3. 7
  4. 6
Answer

B. 4 774 = 11 × 70 + 4.

12. Three bells ring at intervals of 15, 20 and 9 minutes. If they ring together now, after how many minutes will they next ring together?

  1. 300 minutes
  2. 90 minutes
  3. 180 minutes
  4. 44 minutes
Answer

C. 180 minutes LCM(15, 20, 9) = 180 minutes.

13. What is the sum of the first 52 natural numbers?

  1. 2756
  2. 1378
  3. 1430
  4. 2704
Answer

B. 1378 n(n + 1)/2 = 52 × 53/2 = 1378.

14. Find the HCF of 25 and 45.

  1. 6
  2. 4
  3. 5
  4. 45
Answer

C. 5 25 = 5 × 5 and 45 = 5 × 9; 5 and 9 share no factor, so HCF = 5.

15. What is the unit digit of 9^76?

  1. 1
  2. 0
  3. 8
  4. 2
Answer

A. 1 Unit digits of 9^n repeat as 9, 1. 76 gives position 4 in the cycle, so 1.

16. What is the remainder when 818 is divided by 9?

  1. 7
  2. 9
  3. 8
  4. 1
Answer

C. 8 818 = 9 × 90 + 8.

17. Three bells ring at intervals of 8, 10 and 12 minutes. If they ring together now, after how many minutes will they next ring together?

  1. 80 minutes
  2. 128 minutes
  3. 120 minutes
  4. 30 minutes
Answer

C. 120 minutes LCM(8, 10, 12) = 120 minutes.

18. What is the sum of the first 30 natural numbers?

  1. 435
  2. 495
  3. 900
  4. 465
Answer

D. 465 n(n + 1)/2 = 30 × 31/2 = 465.

19. Find the HCF of 18 and 63.

  1. 10
  2. 9
  3. 18
  4. 14
Answer

B. 9 18 = 9 × 2 and 63 = 9 × 7; 2 and 7 share no factor, so HCF = 9.

20. What is the unit digit of 2^54?

  1. 1
  2. 8
  3. 7
  4. 4
Answer

D. 4 Unit digits of 2^n repeat as 2, 4, 8, 6. 54 gives position 2 in the cycle, so 4.

21. What is the remainder when 428 is divided by 14?

  1. 10
  2. 6
  3. 11
  4. 8
Answer

D. 8 428 = 14 × 30 + 8.

22. Three bells ring at intervals of 18, 20 and 4 minutes. If they ring together now, after how many minutes will they next ring together?

  1. 180 minutes
  2. 360 minutes
  3. 90 minutes
  4. 198 minutes
Answer

A. 180 minutes LCM(18, 20, 4) = 180 minutes.

23. What is the sum of the first 56 natural numbers?

  1. 1652
  2. 3192
  3. 1596
  4. 1540
Answer

C. 1596 n(n + 1)/2 = 56 × 57/2 = 1596.

24. Find the HCF of 70 and 50.

  1. 9
  2. 20
  3. 10
  4. 35
Answer

C. 10 70 = 10 × 7 and 50 = 10 × 5; 7 and 5 share no factor, so HCF = 10.

25. What is the unit digit of 8^72?

  1. 3
  2. 2
  3. 6
  4. 1
Answer

C. 6 Unit digits of 8^n repeat as 8, 4, 2, 6. 72 gives position 4 in the cycle, so 6.

26. What is the remainder when 803 is divided by 16?

  1. 4
  2. 3
  3. 6
  4. 13
Answer

B. 3 803 = 16 × 50 + 3.

27. Three bells ring at intervals of 12, 10 and 8 minutes. If they ring together now, after how many minutes will they next ring together?

  1. 132 minutes
  2. 30 minutes
  3. 240 minutes
  4. 120 minutes
Answer

D. 120 minutes LCM(12, 10, 8) = 120 minutes.

28. What is the sum of the first 55 natural numbers?

  1. 3080
  2. 1595
  3. 1540
  4. 1485
Answer

C. 1540 n(n + 1)/2 = 55 × 56/2 = 1540.

29. Find the HCF of 20 and 15.

  1. 20
  2. 5
  3. 6
  4. 12
Answer

B. 5 20 = 5 × 4 and 15 = 5 × 3; 4 and 3 share no factor, so HCF = 5.

30. What is the unit digit of 5^32?

  1. 5
  2. 2
  3. 8
  4. 7
Answer

A. 5 Unit digits of 5^n repeat as 5. 32 gives position 4 in the cycle, so 5.

31. What is the remainder when 814 is divided by 8?

  1. 7
  2. 6
  3. 5
  4. 2
Answer

B. 6 814 = 8 × 101 + 6.

32. Three bells ring at intervals of 16, 15 and 9 minutes. If they ring together now, after how many minutes will they next ring together?

  1. 360 minutes
  2. 720 minutes
  3. 1440 minutes
  4. 240 minutes
Answer

B. 720 minutes LCM(16, 15, 9) = 720 minutes.

33. What is the sum of the first 49 natural numbers?

  1. 2401
  2. 1274
  3. 1176
  4. 1225
Answer

D. 1225 n(n + 1)/2 = 49 × 50/2 = 1225.

34. Find the HCF of 48 and 56.

  1. 8
  2. 9
  3. 16
  4. 42
Answer

A. 8 48 = 8 × 6 and 56 = 8 × 7; 6 and 7 share no factor, so HCF = 8.

35. What is the unit digit of 9^31?

  1. 9
  2. 4
  3. 8
  4. 2
Answer

A. 9 Unit digits of 9^n repeat as 9, 1. 31 gives position 3 in the cycle, so 9.

36. What is the remainder when 925 is divided by 8?

  1. 7
  2. 4
  3. 5
  4. 6
Answer

C. 5 925 = 8 × 115 + 5.

37. Three bells ring at intervals of 16, 5 and 15 minutes. If they ring together now, after how many minutes will they next ring together?

  1. 120 minutes
  2. 480 minutes
  3. 240 minutes
  4. 256 minutes
Answer

C. 240 minutes LCM(16, 5, 15) = 240 minutes.

38. What is the sum of the first 45 natural numbers?

  1. 1080
  2. 1035
  3. 2025
  4. 2070
Answer

B. 1035 n(n + 1)/2 = 45 × 46/2 = 1035.

39. Find the HCF of 9 and 6.

  1. 4
  2. 9
  3. 6
  4. 3
Answer

D. 3 9 = 3 × 3 and 6 = 3 × 2; 3 and 2 share no factor, so HCF = 3.

40. What is the unit digit of 5^59?

  1. 0
  2. 4
  3. 1
  4. 5
Answer

D. 5 Unit digits of 5^n repeat as 5. 59 gives position 3 in the cycle, so 5.

41. What is the remainder when 777 is divided by 12?

  1. 11
  2. 8
  3. 3
  4. 9
Answer

D. 9 777 = 12 × 64 + 9.

42. Three bells ring at intervals of 5, 15 and 20 minutes. If they ring together now, after how many minutes will they next ring together?

  1. 40 minutes
  2. 120 minutes
  3. 30 minutes
  4. 60 minutes
Answer

D. 60 minutes LCM(5, 15, 20) = 60 minutes.

43. What is the sum of the first 50 natural numbers?

  1. 1225
  2. 1275
  3. 1325
  4. 2500
Answer

B. 1275 n(n + 1)/2 = 50 × 51/2 = 1275.

44. Find the HCF of 36 and 45.

  1. 8
  2. 18
  3. 9
  4. 36
Answer

C. 9 36 = 9 × 4 and 45 = 9 × 5; 4 and 5 share no factor, so HCF = 9.

45. What is the unit digit of 7^20?

  1. 6
  2. 0
  3. 1
  4. 5
Answer

C. 1 Unit digits of 7^n repeat as 7, 9, 3, 1. 20 gives position 4 in the cycle, so 1.

46. What is the remainder when 593 is divided by 9?

  1. 1
  2. 8
  3. 9
  4. 7
Answer

B. 8 593 = 9 × 65 + 8.

47. What is the sum of the first 17 natural numbers?

  1. 306
  2. 136
  3. 153
  4. 289
Answer

C. 153 n(n + 1)/2 = 17 × 18/2 = 153.

48. What is the unit digit of 6^20?

  1. 6
  2. 8
  3. 9
  4. 5
Answer

A. 6 Unit digits of 6^n repeat as 6. 20 gives position 4 in the cycle, so 6.

49. What is the sum of the first 33 natural numbers?

  1. 528
  2. 1089
  3. 1122
  4. 561
Answer

D. 561 n(n + 1)/2 = 33 × 34/2 = 561.

50. What is the unit digit of 7^42?

  1. 8
  2. 9
  3. 3
  4. 1
Answer

B. 9 Unit digits of 7^n repeat as 7, 9, 3, 1. 42 gives position 2 in the cycle, so 9.

51. What is the remainder when 764 is divided by 38?

  1. 1
  2. 3
  3. 4
  4. 7
Answer

C. 4 764 = 38×20+4; remainder = 4.

52. What is the remainder when 1711 is divided by 106?

  1. 8
  2. 22
  3. 25
  4. 15
Answer

D. 15 1711 = 106×16+15; remainder = 15.

53. What is the remainder when 408 is divided by 29?

  1. 2
  2. 1
  3. 5
  4. 4
Answer

A. 2 408 = 29×14+2; remainder = 2.

54. What is the remainder when 783 is divided by 97?

  1. 0
  2. 12
  3. 7
  4. 5
Answer

C. 7 783 = 97×8+7; remainder = 7.

55. What is the remainder when 731 is divided by 66?

  1. 10
  2. 4
  3. 3
  4. 5
Answer

D. 5 731 = 66×11+5; remainder = 5.

56. What is the remainder when 2053 is divided by 120?

  1. 13
  2. 10
  3. 23
  4. 3
Answer

A. 13 2053 = 120×17+13; remainder = 13.

57. What is the remainder when 1334 is divided by 78?

  1. 9
  2. 6
  3. 8
  4. 7
Answer

C. 8 1334 = 78×17+8; remainder = 8.

58. What is the remainder when 350 is divided by 116?

  1. 7
  2. 0
  3. 2
  4. 3
Answer

C. 2 350 = 116×3+2; remainder = 2.

59. What is the remainder when 716 is divided by 117?

  1. 4
  2. 14
  3. 12
  4. 21
Answer

B. 14 716 = 117×6+14; remainder = 14.

60. What is the remainder when 33 is divided by 14?

  1. 3
  2. 8
  3. 5
  4. 10
Answer

C. 5 33 = 14×2+5; remainder = 5.

61. What is the remainder when 2295 is divided by 120?

  1. 8
  2. 15
  3. 16
  4. 25
Answer

B. 15 2295 = 120×19+15; remainder = 15.

62. What is the remainder when 1210 is divided by 109?

  1. 11
  2. 4
  3. 13
  4. 8
Answer

A. 11 1210 = 109×11+11; remainder = 11.

63. What is the HCF (GCD) of 18 and 102?

  1. 21
  2. 46
  3. 6
  4. 81
Answer

C. 6 Using Euclid’s algorithm, gcd(18, 102) = 6.

64. Evaluate 54 + 90 × 77 using standard order of operations.

  1. 6985
  2. 6909
  3. 6984
  4. 6982
Answer

C. 6984 Multiplication first: 90 × 77 = 6930; add 54 to get 6984.

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