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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 469 · 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 60 to 86? (a) 13 (b) 74 (c) 26 (d) 73
  2. 2.What is the average of all the whole numbers from 51 to 73? (a) 63 (b) 22 (c) 62 (d) 11
  3. 3.What is the average of all the whole numbers from 18 to 24? (a) 21 (b) 6 (c) 22 (d) 3
  4. 4.A batter has an average of 48 runs in 6 matches. How many runs are needed in the next match to raise the average to 56? (a) 105 (b) 104 (c) 56 (d) 64
  5. 5.A batter has an average of 41 runs in 4 matches. How many runs are needed in the next match to raise the average to 45? (a) 20 (b) 61 (c) 45 (d) 49
  6. 6.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) 38 (c) 102 (d) 37
  7. 7.The average of 5 numbers is 20. When one number is taken away, the average of the rest is 23. Which number was taken away? (a) 20 (b) 43 (c) 8 (d) 9
  8. 8.What is the average of all the whole numbers from 28 to 40? (a) 34 (b) 6 (c) 35 (d) 12
  9. 9.The average of 7 numbers is 27. When one number is taken away, the average of the rest is 24. Which number was taken away? (a) 45 (b) 51 (c) 21 (d) 27
  10. 10.The average of 5 numbers is 21. When one number is taken away, the average of the rest is 20. Which number was taken away? (a) 41 (b) 5 (c) 21 (d) 25
  11. 11.What is the average of all the whole numbers from 23 to 29? (a) 27 (b) 3 (c) 26 (d) 6
  12. 12.A batter has an average of 45 runs in 9 matches. How many runs are needed in the next match to raise the average to 47? (a) 65 (b) 47 (c) 20 (d) 49
  13. 13.What is the average of all the whole numbers from 8 to 42? (a) 26 (b) 25 (c) 34 (d) 17
  14. 14.What is the average of 45, 47, 61, 55, 55 and 61? (a) 56 (b) 55 (c) 54 (d) 53
  15. 15.What is the average of all the whole numbers from 19 to 49? (a) 35 (b) 15 (c) 34 (d) 30
  16. 16.The average of 6 numbers is 34. When one number is taken away, the average of the rest is 39. Which number was taken away? (a) 10 (b) 34 (c) 73 (d) 9
  17. 17.A batter has an average of 43 runs in 8 matches. How many runs are needed in the next match to raise the average to 48? (a) 48 (b) 53 (c) 88 (d) 45
  18. 18.The average of 6 numbers is 16. When one number is taken away, the average of the rest is 14. Which number was taken away? (a) 12 (b) 26 (c) 16 (d) 30
  19. 19.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) 4 (b) 28 (c) 55 (d) 31
  20. 20.What is the average of 54, 74, 52 and 72? (a) 63 (b) 64 (c) 84 (d) 62
  21. 21.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 27? (a) 27 (b) 32 (c) 25 (d) 47
  22. 22.What is the average of all the whole numbers from 13 to 35? (a) 24 (b) 11 (c) 22 (d) 25
  23. 23.What is the average of 32, 33, 36, 28, 38 and 67? (a) 40 (b) 41 (c) 39 (d) 38
  24. 24.What is the average of 32, 23, 28 and 57? (a) 36 (b) 37 (c) 34 (d) 35
  25. 25.The average of 5 numbers is 22. When one number is taken away, the average of the rest is 27. Which number was taken away? (a) 22 (b) 3 (c) 2 (d) 49
  26. 26.The average of 7 numbers is 10. When one number is taken away, the average of the rest is 7. Which number was taken away? (a) 17 (b) 10 (c) 21 (d) 28
  27. 27.What is the average of 53, 63, 50, 51 and 103? (a) 65 (b) 80 (c) 63 (d) 64
  28. 28.What is the average of all the whole numbers from 40 to 54? (a) 7 (b) 14 (c) 47 (d) 48
  29. 29.The average of 7 numbers is 32. When one number is taken away, the average of the rest is 35. Which number was taken away? (a) 14 (b) 32 (c) 15 (d) 67
  30. 30.What is the average of all the whole numbers from 12 to 22? (a) 5 (b) 18 (c) 10 (d) 17
  31. 31.What is the average of 48, 52, 39, 49, 50 and 80? (a) 54 (b) 53 (c) 55 (d) 52
  32. 32.What is the average of 61, 74, 78 and 63? (a) 68 (b) 69 (c) 70 (d) 92
  33. 33.The average of 6 numbers is 42. When one number is taken away, the average of the rest is 45. Which number was taken away? (a) 28 (b) 27 (c) 87 (d) 42
  34. 34.The average of 6 numbers is 27. When one number is taken away, the average of the rest is 31. Which number was taken away? (a) 58 (b) 7 (c) 27 (d) 8
  35. 35.What is the average of 35, 51, 41 and 41? (a) 43 (b) 41 (c) 42 (d) 56
  36. 36.What is the average of 74, 60, 56, 58 and 107? (a) 72 (b) 71 (c) 70 (d) 73
  37. 37.What is the average of all the whole numbers from 29 to 41? (a) 36 (b) 35 (c) 6 (d) 12
  38. 38.What is the average of 42, 47, 42, 56, 54 and 83? (a) 55 (b) 53 (c) 56 (d) 54
  39. 39.What is the average of 73, 62, 82 and 71? (a) 73 (b) 96 (c) 72 (d) 71
  40. 40.What is the average of 46, 37, 39, 60 and 78? (a) 52 (b) 51 (c) 53 (d) 65

Answer key

  1. 73
  2. 62
  3. 21
  4. 104
  5. 61
  6. 37
  7. 8
  8. 34
  9. 45
  10. 25
  11. 26
  12. 65
  13. 25
  14. 54
  15. 34
  16. 9
  17. 88
  18. 26
  19. 31
  20. 63
  21. 47
  22. 24
  23. 39
  24. 35
  25. 2
  26. 28
  27. 64
  28. 47
  29. 14
  30. 17
  31. 53
  32. 69
  33. 27
  34. 7
  35. 42
  36. 71
  37. 35
  38. 54
  39. 72
  40. 52

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