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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 15 · 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 58 to 98? (a) 78 (b) 79 (c) 20 (d) 40
  2. 2.What is the average of 51, 60, 32 and 45? (a) 49 (b) 46 (c) 48 (d) 47
  3. 3.The average of 4 numbers is 26. When one number is taken away, the average of the rest is 31. Which number was taken away? (a) 12 (b) 26 (c) 11 (d) 57
  4. 4.A batter has an average of 42 runs in 7 matches. How many runs are needed in the next match to raise the average to 49? (a) 99 (b) 49 (c) 98 (d) 56
  5. 5.A batter has an average of 50 runs in 6 matches. How many runs are needed in the next match to raise the average to 53? (a) 71 (b) 56 (c) 21 (d) 53
  6. 6.What is the average of all the whole numbers from 33 to 55? (a) 45 (b) 44 (c) 22 (d) 11
  7. 7.What is the average of all the whole numbers from 16 to 38? (a) 11 (b) 22 (c) 27 (d) 28
  8. 8.A batter has an average of 54 runs in 9 matches. How many runs are needed in the next match to raise the average to 61? (a) 124 (b) 70 (c) 61 (d) 68
  9. 9.What is the average of 83, 81, 76 and 60? (a) 75 (b) 74 (c) 76 (d) 100
  10. 10.What is the average of 82, 61, 67 and 66? (a) 70 (b) 68 (c) 92 (d) 69
  11. 11.What is the average of all the whole numbers from 5 to 29? (a) 17 (b) 12 (c) 24 (d) 18
  12. 12.What is the average of 65, 72, 75 and 48? (a) 67 (b) 65 (c) 66 (d) 64
  13. 13.The average of 4 numbers is 17. When one number is taken away, the average of the rest is 21. Which number was taken away? (a) 17 (b) 5 (c) 6 (d) 38
  14. 14.What is the average of all the whole numbers from 56 to 82? (a) 13 (b) 26 (c) 69 (d) 70
  15. 15.What is the average of 17, 25, 27, 8 and 38? (a) 22 (b) 23 (c) 24 (d) 25
  16. 16.What is the average of all the whole numbers from 37 to 71? (a) 34 (b) 17 (c) 55 (d) 54
  17. 17.A batter has an average of 58 runs in 8 matches. How many runs are needed in the next match to raise the average to 61? (a) 64 (b) 85 (c) 27 (d) 61
  18. 18.A batter has an average of 22 runs in 3 matches. How many runs are needed in the next match to raise the average to 25? (a) 12 (b) 28 (c) 34 (d) 25
  19. 19.What is the average of all the whole numbers from 30 to 36? (a) 6 (b) 33 (c) 34 (d) 3
  20. 20.What is the average of all the whole numbers from 37 to 51? (a) 44 (b) 45 (c) 14 (d) 7
  21. 21.A batter has an average of 43 runs in 9 matches. How many runs are needed in the next match to raise the average to 48? (a) 50 (b) 53 (c) 48 (d) 93
  22. 22.The average of 8 numbers is 22. When one number is taken away, the average of the rest is 23. Which number was taken away? (a) 45 (b) 16 (c) 15 (d) 22
  23. 23.What is the average of all the whole numbers from 45 to 79? (a) 63 (b) 17 (c) 34 (d) 62
  24. 24.A batter has an average of 58 runs in 7 matches. How many runs are needed in the next match to raise the average to 64? (a) 64 (b) 48 (c) 106 (d) 70
  25. 25.The average of 8 numbers is 31. When one number is taken away, the average of the rest is 32. Which number was taken away? (a) 24 (b) 63 (c) 25 (d) 31
  26. 26.What is the average of 36, 53, 40 and 67? (a) 50 (b) 51 (c) 48 (d) 49
  27. 27.What is the average of all the whole numbers from 33 to 41? (a) 4 (b) 8 (c) 37 (d) 38
  28. 28.What is the average of all the whole numbers from 50 to 64? (a) 14 (b) 58 (c) 7 (d) 57
  29. 29.The average of 7 numbers is 46. When one number is taken away, the average of the rest is 44. Which number was taken away? (a) 58 (b) 14 (c) 46 (d) 90
  30. 30.The average of 4 numbers is 50. When one number is taken away, the average of the rest is 53. Which number was taken away? (a) 42 (b) 103 (c) 41 (d) 50
  31. 31.A batter has an average of 36 runs in 8 matches. How many runs are needed in the next match to raise the average to 39? (a) 39 (b) 42 (c) 63 (d) 27
  32. 32.A batter has an average of 44 runs in 3 matches. How many runs are needed in the next match to raise the average to 51? (a) 72 (b) 58 (c) 51 (d) 28
  33. 33.What is the average of 37, 54, 42 and 47? (a) 44 (b) 60 (c) 46 (d) 45
  34. 34.What is the average of all the whole numbers from 13 to 43? (a) 15 (b) 30 (c) 28 (d) 29
  35. 35.A batter has an average of 31 runs in 3 matches. How many runs are needed in the next match to raise the average to 34? (a) 34 (b) 12 (c) 43 (d) 37
  36. 36.The average of 6 numbers is 34. When one number is taken away, the average of the rest is 33. Which number was taken away? (a) 39 (b) 6 (c) 34 (d) 67
  37. 37.What is the average of 31, 33, 51, 49 and 36? (a) 41 (b) 50 (c) 40 (d) 39
  38. 38.What is the average of 57, 80, 59 and 84? (a) 72 (b) 69 (c) 71 (d) 70
  39. 39.What is the average of 42, 52, 58, 39, 48 and 61? (a) 50 (b) 60 (c) 49 (d) 51
  40. 40.What is the average of all the whole numbers from 47 to 77? (a) 62 (b) 30 (c) 63 (d) 15

Answer key

  1. 78
  2. 47
  3. 11
  4. 98
  5. 71
  6. 44
  7. 27
  8. 124
  9. 75
  10. 69
  11. 17
  12. 65
  13. 5
  14. 69
  15. 23
  16. 54
  17. 85
  18. 34
  19. 33
  20. 44
  21. 93
  22. 15
  23. 62
  24. 106
  25. 24
  26. 49
  27. 37
  28. 57
  29. 58
  30. 41
  31. 63
  32. 72
  33. 45
  34. 28
  35. 43
  36. 39
  37. 40
  38. 70
  39. 50
  40. 62

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