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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 949 · 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.What is the average of all the whole numbers from 27 to 33? (a) 3 (b) 30 (c) 31 (d) 6
  2. 2.A batter has an average of 58 runs in 9 matches. How many runs are needed in the next match to raise the average to 65? (a) 65 (b) 72 (c) 128 (d) 70
  3. 3.A batter has an average of 21 runs in 8 matches. How many runs are needed in the next match to raise the average to 27? (a) 33 (b) 75 (c) 27 (d) 54
  4. 4.What is the average of 53, 37, 42, 39, 36 and 81? (a) 50 (b) 49 (c) 47 (d) 48
  5. 5.What is the average of 53, 33, 34, 48, 45 and 39? (a) 42 (b) 43 (c) 41 (d) 44
  6. 6.What is the average of 53, 66, 67 and 74? (a) 66 (b) 65 (c) 67 (d) 64
  7. 7.The average of 7 numbers is 43. When one number is taken away, the average of the rest is 39. Which number was taken away? (a) 28 (b) 43 (c) 82 (d) 67
  8. 8.What is the average of all the whole numbers from 50 to 78? (a) 65 (b) 64 (c) 28 (d) 14
  9. 9.The average of 7 numbers is 22. When one number is taken away, the average of the rest is 20. Which number was taken away? (a) 22 (b) 34 (c) 42 (d) 14
  10. 10.The average of 7 numbers is 32. When one number is taken away, the average of the rest is 31. Which number was taken away? (a) 7 (b) 38 (c) 63 (d) 32
  11. 11.What is the average of 40, 39, 59, 36, 51 and 45? (a) 54 (b) 46 (c) 44 (d) 45
  12. 12.What is the average of 66, 72, 82, 64 and 76? (a) 72 (b) 73 (c) 90 (d) 71
  13. 13.What is the average of all the whole numbers from 17 to 55? (a) 19 (b) 36 (c) 37 (d) 38
  14. 14.The average of 6 numbers is 45. When one number is taken away, the average of the rest is 44. Which number was taken away? (a) 50 (b) 6 (c) 45 (d) 89
  15. 15.The average of 6 numbers is 49. When one number is taken away, the average of the rest is 46. Which number was taken away? (a) 64 (b) 49 (c) 18 (d) 95
  16. 16.What is the average of all the whole numbers from 13 to 47? (a) 31 (b) 17 (c) 34 (d) 30
  17. 17.What is the average of all the whole numbers from 10 to 16? (a) 13 (b) 14 (c) 3 (d) 6
  18. 18.The average of 4 numbers is 33. When one number is taken away, the average of the rest is 34. Which number was taken away? (a) 31 (b) 33 (c) 30 (d) 67
  19. 19.The average of 4 numbers is 17. When one number is taken away, the average of the rest is 22. Which number was taken away? (a) 17 (b) 39 (c) 3 (d) 2
  20. 20.What is the average of 18, 30, 9, 28 and 25? (a) 23 (b) 24 (c) 21 (d) 22
  21. 21.What is the average of 31, 56, 34, 48, 58 and 49? (a) 47 (b) 48 (c) 46 (d) 45
  22. 22.A batter has an average of 45 runs in 3 matches. How many runs are needed in the next match to raise the average to 53? (a) 53 (b) 77 (c) 61 (d) 32
  23. 23.A batter has an average of 59 runs in 4 matches. How many runs are needed in the next match to raise the average to 67? (a) 40 (b) 99 (c) 75 (d) 67
  24. 24.What is the average of 50, 34, 57 and 27? (a) 56 (b) 41 (c) 43 (d) 42
  25. 25.What is the average of all the whole numbers from 41 to 53? (a) 6 (b) 48 (c) 12 (d) 47
  26. 26.What is the average of 65, 57, 49, 50 and 74? (a) 59 (b) 60 (c) 58 (d) 61
  27. 27.What is the average of all the whole numbers from 46 to 80? (a) 63 (b) 64 (c) 17 (d) 34
  28. 28.What is the average of 60, 65, 73 and 86? (a) 72 (b) 70 (c) 73 (d) 71
  29. 29.What is the average of 25, 40, 35 and 8? (a) 27 (b) 36 (c) 28 (d) 26
  30. 30.The average of 6 numbers is 21. When one number is taken away, the average of the rest is 19. Which number was taken away? (a) 12 (b) 21 (c) 31 (d) 40
  31. 31.What is the average of all the whole numbers from 31 to 65? (a) 34 (b) 17 (c) 48 (d) 49
  32. 32.What is the average of all the whole numbers from 57 to 93? (a) 75 (b) 36 (c) 18 (d) 76
  33. 33.What is the average of 48, 70, 67, 67, 71 and 13? (a) 58 (b) 57 (c) 55 (d) 56
  34. 34.The average of 7 numbers is 21. When one number is taken away, the average of the rest is 19. Which number was taken away? (a) 21 (b) 40 (c) 14 (d) 33
  35. 35.What is the average of all the whole numbers from 27 to 43? (a) 16 (b) 8 (c) 35 (d) 36
  36. 36.The average of 8 numbers is 32. When one number is taken away, the average of the rest is 34. Which number was taken away? (a) 18 (b) 19 (c) 66 (d) 32
  37. 37.What is the average of all the whole numbers from 42 to 66? (a) 55 (b) 12 (c) 24 (d) 54
  38. 38.The average of 7 numbers is 43. When one number is taken away, the average of the rest is 47. Which number was taken away? (a) 43 (b) 19 (c) 20 (d) 90
  39. 39.What is the average of all the whole numbers from 22 to 30? (a) 26 (b) 27 (c) 4 (d) 8
  40. 40.The average of 4 numbers is 18. When one number is taken away, the average of the rest is 23. Which number was taken away? (a) 18 (b) 3 (c) 41 (d) 4

Answer key

  1. 30
  2. 128
  3. 75
  4. 48
  5. 42
  6. 65
  7. 67
  8. 64
  9. 34
  10. 38
  11. 45
  12. 72
  13. 36
  14. 50
  15. 64
  16. 30
  17. 13
  18. 30
  19. 2
  20. 22
  21. 46
  22. 77
  23. 99
  24. 42
  25. 47
  26. 59
  27. 63
  28. 71
  29. 27
  30. 31
  31. 48
  32. 75
  33. 56
  34. 33
  35. 35
  36. 18
  37. 54
  38. 19
  39. 26
  40. 3

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