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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 255 · 40 questions
TalentJR

How to solve it (Think in totals): Average = total ÷ how many; so total = average × how many. A number taken away = old total − new total. Evenly spaced numbers (like 10 to 20): average = (first + last) ÷ 2.

NameDateTime takenScore ___ / 40
  1. 1.The average of 4 numbers is 19. When one number is taken away, the average of the rest is 20. Which number was taken away? (a) 17 (b) 39 (c) 19 (d) 16
  2. 2.What is the average of 66, 89, 82, 74 and 89? (a) 81 (b) 79 (c) 100 (d) 80
  3. 3.The average of 4 numbers is 44. When one number is taken away, the average of the rest is 41. Which number was taken away? (a) 53 (b) 85 (c) 44 (d) 12
  4. 4.The average of 6 numbers is 50. When one number is taken away, the average of the rest is 55. Which number was taken away? (a) 25 (b) 105 (c) 50 (d) 26
  5. 5.The average of 7 numbers is 35. When one number is taken away, the average of the rest is 33. Which number was taken away? (a) 68 (b) 47 (c) 35 (d) 14
  6. 6.What is the average of all the whole numbers from 30 to 44? (a) 38 (b) 14 (c) 37 (d) 7
  7. 7.The average of 8 numbers is 50. When one number is taken away, the average of the rest is 45. Which number was taken away? (a) 95 (b) 40 (c) 85 (d) 50
  8. 8.What is the average of all the whole numbers from 52 to 92? (a) 72 (b) 40 (c) 20 (d) 73
  9. 9.What is the average of 31, 40, 39, 18, 43 and 3? (a) 30 (b) 29 (c) 31 (d) 28
  10. 10.What is the average of 64, 84, 59, 71, 69 and 91? (a) 72 (b) 74 (c) 75 (d) 73
  11. 11.What is the average of 60, 67, 52, 55, 50 and 64? (a) 59 (b) 57 (c) 60 (d) 58
  12. 12.The average of 7 numbers is 26. When one number is taken away, the average of the rest is 29. Which number was taken away? (a) 9 (b) 8 (c) 55 (d) 26
  13. 13.What is the average of 31, 30, 30 and 69? (a) 39 (b) 41 (c) 42 (d) 40
  14. 14.The average of 4 numbers is 28. When one number is taken away, the average of the rest is 27. Which number was taken away? (a) 55 (b) 28 (c) 4 (d) 31
  15. 15.What is the average of all the whole numbers from 42 to 64? (a) 54 (b) 53 (c) 22 (d) 11
  16. 16.What is the average of 68, 75, 54, 51, 49 and 75? (a) 62 (b) 64 (c) 61 (d) 63
  17. 17.A batter has an average of 47 runs in 7 matches. How many runs are needed in the next match to raise the average to 53? (a) 53 (b) 48 (c) 95 (d) 59
  18. 18.What is the average of 57, 65, 64 and 58? (a) 60 (b) 61 (c) 63 (d) 62
  19. 19.What is the average of 21, 18, 34, 8, 30 and 27? (a) 24 (b) 22 (c) 23 (d) 25
  20. 20.What is the average of 32, 54, 43, 37 and 69? (a) 47 (b) 46 (c) 48 (d) 49
  21. 21.The average of 4 numbers is 29. When one number is taken away, the average of the rest is 24. Which number was taken away? (a) 29 (b) 20 (c) 53 (d) 44
  22. 22.What is the average of 63, 70, 64 and 115? (a) 79 (b) 77 (c) 78 (d) 104
  23. 23.A batter has an average of 42 runs in 8 matches. How many runs are needed in the next match to raise the average to 47? (a) 45 (b) 52 (c) 87 (d) 47
  24. 24.What is the average of 37, 47, 34, 45 and 17? (a) 36 (b) 37 (c) 45 (d) 35
  25. 25.What is the average of all the whole numbers from 52 to 60? (a) 57 (b) 56 (c) 8 (d) 4
  26. 26.What is the average of all the whole numbers from 8 to 38? (a) 24 (b) 23 (c) 15 (d) 30
  27. 27.What is the average of all the whole numbers from 5 to 15? (a) 9 (b) 5 (c) 11 (d) 10
  28. 28.The average of 7 numbers is 48. When one number is taken away, the average of the rest is 49. Which number was taken away? (a) 42 (b) 97 (c) 43 (d) 48
  29. 29.The average of 5 numbers is 36. When one number is taken away, the average of the rest is 35. Which number was taken away? (a) 71 (b) 36 (c) 40 (d) 5
  30. 30.What is the average of 50, 25, 45, 37 and 18? (a) 35 (b) 36 (c) 34 (d) 37
  31. 31.The average of 4 numbers is 29. When one number is taken away, the average of the rest is 27. Which number was taken away? (a) 29 (b) 35 (c) 8 (d) 56
  32. 32.What is the average of all the whole numbers from 11 to 49? (a) 30 (b) 31 (c) 19 (d) 38
  33. 33.What is the average of all the whole numbers from 42 to 82? (a) 20 (b) 63 (c) 40 (d) 62
  34. 34.What is the average of all the whole numbers from 17 to 45? (a) 28 (b) 31 (c) 32 (d) 14
  35. 35.What is the average of all the whole numbers from 40 to 70? (a) 15 (b) 55 (c) 56 (d) 30
  36. 36.What is the average of all the whole numbers from 23 to 61? (a) 19 (b) 42 (c) 38 (d) 43
  37. 37.What is the average of 38, 37, 19 and 30? (a) 30 (b) 31 (c) 32 (d) 33
  38. 38.The average of 6 numbers is 44. When one number is taken away, the average of the rest is 49. Which number was taken away? (a) 93 (b) 20 (c) 44 (d) 19
  39. 39.A batter has an average of 29 runs in 6 matches. How many runs are needed in the next match to raise the average to 31? (a) 33 (b) 31 (c) 14 (d) 43
  40. 40.What is the average of 77, 63, 57 and 55? (a) 64 (b) 62 (c) 63 (d) 84

Answer key

  1. 16
  2. 80
  3. 53
  4. 25
  5. 47
  6. 37
  7. 85
  8. 72
  9. 29
  10. 73
  11. 58
  12. 8
  13. 40
  14. 31
  15. 53
  16. 62
  17. 95
  18. 61
  19. 23
  20. 47
  21. 44
  22. 78
  23. 87
  24. 36
  25. 56
  26. 23
  27. 10
  28. 42
  29. 40
  30. 35
  31. 35
  32. 30
  33. 62
  34. 31
  35. 55
  36. 42
  37. 31
  38. 19
  39. 43
  40. 63

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