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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 65 · 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 18, 43, 16 and 39? (a) 31 (b) 29 (c) 28 (d) 30
  2. 2.What is the average of all the whole numbers from 55 to 73? (a) 9 (b) 65 (c) 18 (d) 64
  3. 3.What is the average of all the whole numbers from 27 to 35? (a) 31 (b) 32 (c) 8 (d) 4
  4. 4.The average of 8 numbers is 30. When one number is taken away, the average of the rest is 31. Which number was taken away? (a) 23 (b) 24 (c) 61 (d) 30
  5. 5.A batter has an average of 56 runs in 3 matches. How many runs are needed in the next match to raise the average to 64? (a) 32 (b) 64 (c) 72 (d) 88
  6. 6.What is the average of all the whole numbers from 18 to 36? (a) 18 (b) 9 (c) 27 (d) 28
  7. 7.What is the average of 63, 75, 84 and 54? (a) 70 (b) 68 (c) 69 (d) 92
  8. 8.The average of 5 numbers is 30. When one number is taken away, the average of the rest is 32. Which number was taken away? (a) 30 (b) 22 (c) 62 (d) 23
  9. 9.What is the average of 32, 13, 17 and 34? (a) 32 (b) 23 (c) 25 (d) 24
  10. 10.The average of 4 numbers is 12. When one number is taken away, the average of the rest is 15. Which number was taken away? (a) 4 (b) 27 (c) 3 (d) 12
  11. 11.What is the average of 52, 57, 55, 48, 50 and 116? (a) 64 (b) 62 (c) 63 (d) 65
  12. 12.A batter has an average of 37 runs in 4 matches. How many runs are needed in the next match to raise the average to 45? (a) 40 (b) 77 (c) 45 (d) 53
  13. 13.What is the average of all the whole numbers from 58 to 74? (a) 66 (b) 67 (c) 8 (d) 16
  14. 14.The average of 7 numbers is 34. When one number is taken away, the average of the rest is 39. Which number was taken away? (a) 73 (b) 34 (c) 5 (d) 4
  15. 15.A batter has an average of 43 runs in 7 matches. How many runs are needed in the next match to raise the average to 48? (a) 40 (b) 48 (c) 83 (d) 53
  16. 16.What is the average of all the whole numbers from 5 to 19? (a) 14 (b) 12 (c) 7 (d) 13
  17. 17.What is the average of 64, 58, 68, 48, 54 and 80? (a) 61 (b) 63 (c) 62 (d) 64
  18. 18.What is the average of 21, 25, 32 and 66? (a) 35 (b) 37 (c) 36 (d) 48
  19. 19.A batter has an average of 23 runs in 4 matches. How many runs are needed in the next match to raise the average to 27? (a) 27 (b) 31 (c) 43 (d) 20
  20. 20.The average of 6 numbers is 27. When one number is taken away, the average of the rest is 28. Which number was taken away? (a) 27 (b) 23 (c) 55 (d) 22
  21. 21.What is the average of all the whole numbers from 58 to 72? (a) 7 (b) 14 (c) 65 (d) 66
  22. 22.The average of 6 numbers is 21. When one number is taken away, the average of the rest is 24. Which number was taken away? (a) 7 (b) 45 (c) 6 (d) 21
  23. 23.What is the average of 45, 49, 34, 64, 34 and 68? (a) 51 (b) 48 (c) 49 (d) 50
  24. 24.The average of 7 numbers is 27. When one number is taken away, the average of the rest is 25. Which number was taken away? (a) 52 (b) 14 (c) 27 (d) 39
  25. 25.The average of 4 numbers is 33. When one number is taken away, the average of the rest is 38. Which number was taken away? (a) 71 (b) 18 (c) 33 (d) 19
  26. 26.What is the average of 53, 34, 55 and 54? (a) 50 (b) 49 (c) 51 (d) 48
  27. 27.The average of 6 numbers is 34. When one number is taken away, the average of the rest is 30. Which number was taken away? (a) 64 (b) 24 (c) 54 (d) 34
  28. 28.What is the average of 86, 57, 56 and 85? (a) 73 (b) 72 (c) 70 (d) 71
  29. 29.What is the average of 18, 35, 13, 20, 12 and 52? (a) 25 (b) 24 (c) 30 (d) 26
  30. 30.What is the average of all the whole numbers from 10 to 22? (a) 17 (b) 16 (c) 6 (d) 12
  31. 31.What is the average of 33, 23, 41, 26, 32 and 61? (a) 37 (b) 35 (c) 36 (d) 38
  32. 32.The average of 4 numbers is 49. When one number is taken away, the average of the rest is 53. Which number was taken away? (a) 49 (b) 37 (c) 102 (d) 38
  33. 33.A batter has an average of 22 runs in 4 matches. How many runs are needed in the next match to raise the average to 28? (a) 52 (b) 34 (c) 30 (d) 28
  34. 34.A batter has an average of 44 runs in 7 matches. How many runs are needed in the next match to raise the average to 51? (a) 58 (b) 51 (c) 56 (d) 100
  35. 35.The average of 6 numbers is 11. When one number is taken away, the average of the rest is 10. Which number was taken away? (a) 16 (b) 21 (c) 11 (d) 6
  36. 36.A batter has an average of 56 runs in 8 matches. How many runs are needed in the next match to raise the average to 61? (a) 101 (b) 45 (c) 61 (d) 66
  37. 37.The average of 4 numbers is 43. When one number is taken away, the average of the rest is 41. Which number was taken away? (a) 8 (b) 43 (c) 84 (d) 49
  38. 38.A batter has an average of 57 runs in 4 matches. How many runs are needed in the next match to raise the average to 61? (a) 65 (b) 20 (c) 61 (d) 77
  39. 39.What is the average of 43, 49, 52 and 4? (a) 37 (b) 36 (c) 39 (d) 38
  40. 40.The average of 5 numbers is 24. When one number is taken away, the average of the rest is 22. Which number was taken away? (a) 46 (b) 24 (c) 32 (d) 10

Answer key

  1. 29
  2. 64
  3. 31
  4. 23
  5. 88
  6. 27
  7. 69
  8. 22
  9. 24
  10. 3
  11. 63
  12. 77
  13. 66
  14. 4
  15. 83
  16. 12
  17. 62
  18. 36
  19. 43
  20. 22
  21. 65
  22. 6
  23. 49
  24. 39
  25. 18
  26. 49
  27. 54
  28. 71
  29. 25
  30. 16
  31. 36
  32. 37
  33. 52
  34. 100
  35. 16
  36. 101
  37. 49
  38. 77
  39. 37
  40. 32

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