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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 597 · 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 5 numbers is 20. When one number is taken away, the average of the rest is 18. Which number was taken away? (a) 20 (b) 28 (c) 38 (d) 10
  2. 2.A batter has an average of 49 runs in 3 matches. How many runs are needed in the next match to raise the average to 52? (a) 55 (b) 61 (c) 52 (d) 12
  3. 3.A batter has an average of 36 runs in 3 matches. How many runs are needed in the next match to raise the average to 39? (a) 39 (b) 48 (c) 42 (d) 12
  4. 4.A batter has an average of 59 runs in 8 matches. How many runs are needed in the next match to raise the average to 65? (a) 71 (b) 65 (c) 113 (d) 54
  5. 5.What is the average of 66, 81, 64 and 81? (a) 74 (b) 75 (c) 73 (d) 72
  6. 6.What is the average of 63, 64, 76 and 61? (a) 65 (b) 88 (c) 66 (d) 67
  7. 7.The average of 4 numbers is 37. When one number is taken away, the average of the rest is 39. Which number was taken away? (a) 76 (b) 31 (c) 32 (d) 37
  8. 8.A batter has an average of 50 runs in 8 matches. How many runs are needed in the next match to raise the average to 54? (a) 58 (b) 36 (c) 54 (d) 86
  9. 9.The average of 4 numbers is 39. When one number is taken away, the average of the rest is 44. Which number was taken away? (a) 24 (b) 25 (c) 83 (d) 39
  10. 10.A batter has an average of 22 runs in 7 matches. How many runs are needed in the next match to raise the average to 26? (a) 30 (b) 54 (c) 32 (d) 26
  11. 11.A batter has an average of 31 runs in 4 matches. How many runs are needed in the next match to raise the average to 39? (a) 71 (b) 40 (c) 39 (d) 47
  12. 12.The average of 7 numbers is 45. When one number is taken away, the average of the rest is 44. Which number was taken away? (a) 89 (b) 51 (c) 45 (d) 7
  13. 13.What is the average of 70, 81, 76, 61, 65 and 61? (a) 68 (b) 71 (c) 70 (d) 69
  14. 14.What is the average of all the whole numbers from 14 to 44? (a) 30 (b) 28 (c) 15 (d) 29
  15. 15.What is the average of all the whole numbers from 24 to 54? (a) 30 (b) 15 (c) 40 (d) 39
  16. 16.A batter has an average of 27 runs in 5 matches. How many runs are needed in the next match to raise the average to 30? (a) 33 (b) 45 (c) 30 (d) 18
  17. 17.What is the average of 45, 63, 37, 43, 54 and 70? (a) 52 (b) 51 (c) 53 (d) 54
  18. 18.What is the average of 16, 23, 16 and 69? (a) 31 (b) 33 (c) 30 (d) 32
  19. 19.What is the average of 87, 62, 62, 88 and 66? (a) 72 (b) 75 (c) 74 (d) 73
  20. 20.What is the average of all the whole numbers from 27 to 57? (a) 43 (b) 42 (c) 30 (d) 15
  21. 21.What is the average of all the whole numbers from 20 to 26? (a) 3 (b) 24 (c) 6 (d) 23
  22. 22.The average of 7 numbers is 29. When one number is taken away, the average of the rest is 33. Which number was taken away? (a) 29 (b) 62 (c) 6 (d) 5
  23. 23.The average of 7 numbers is 31. When one number is taken away, the average of the rest is 36. Which number was taken away? (a) 1 (b) 67 (c) 31 (d) 2
  24. 24.A batter has an average of 28 runs in 7 matches. How many runs are needed in the next match to raise the average to 30? (a) 30 (b) 44 (c) 16 (d) 32
  25. 25.A batter has an average of 20 runs in 3 matches. How many runs are needed in the next match to raise the average to 24? (a) 24 (b) 28 (c) 16 (d) 36
  26. 26.A batter has an average of 36 runs in 3 matches. How many runs are needed in the next match to raise the average to 41? (a) 46 (b) 41 (c) 20 (d) 56
  27. 27.What is the average of 73, 65, 76, 67, 78 and 91? (a) 90 (b) 74 (c) 76 (d) 75
  28. 28.The average of 5 numbers is 37. When one number is taken away, the average of the rest is 42. Which number was taken away? (a) 18 (b) 79 (c) 17 (d) 37
  29. 29.The average of 6 numbers is 33. When one number is taken away, the average of the rest is 38. Which number was taken away? (a) 71 (b) 33 (c) 8 (d) 9
  30. 30.What is the average of 64, 69, 67, 67 and 23? (a) 59 (b) 58 (c) 60 (d) 57
  31. 31.The average of 6 numbers is 29. When one number is taken away, the average of the rest is 33. Which number was taken away? (a) 62 (b) 9 (c) 29 (d) 10
  32. 32.The average of 4 numbers is 36. When one number is taken away, the average of the rest is 41. Which number was taken away? (a) 77 (b) 21 (c) 36 (d) 22
  33. 33.The average of 6 numbers is 41. When one number is taken away, the average of the rest is 40. Which number was taken away? (a) 46 (b) 6 (c) 41 (d) 81
  34. 34.A batter has an average of 23 runs in 7 matches. How many runs are needed in the next match to raise the average to 30? (a) 79 (b) 56 (c) 37 (d) 30
  35. 35.What is the average of 25, 29, 28 and 78? (a) 40 (b) 41 (c) 42 (d) 39
  36. 36.What is the average of 47, 54, 70, 50 and 79? (a) 60 (b) 75 (c) 61 (d) 59
  37. 37.What is the average of 30, 38, 30 and 74? (a) 43 (b) 44 (c) 45 (d) 42
  38. 38.What is the average of all the whole numbers from 47 to 75? (a) 62 (b) 28 (c) 61 (d) 14
  39. 39.The average of 4 numbers is 14. When one number is taken away, the average of the rest is 11. Which number was taken away? (a) 14 (b) 25 (c) 23 (d) 12
  40. 40.A batter has an average of 23 runs in 6 matches. How many runs are needed in the next match to raise the average to 26? (a) 29 (b) 44 (c) 26 (d) 21

Answer key

  1. 28
  2. 61
  3. 48
  4. 113
  5. 73
  6. 66
  7. 31
  8. 86
  9. 24
  10. 54
  11. 71
  12. 51
  13. 69
  14. 29
  15. 39
  16. 45
  17. 52
  18. 31
  19. 73
  20. 42
  21. 23
  22. 5
  23. 1
  24. 44
  25. 36
  26. 56
  27. 75
  28. 17
  29. 8
  30. 58
  31. 9
  32. 21
  33. 46
  34. 79
  35. 40
  36. 60
  37. 43
  38. 61
  39. 23
  40. 44

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