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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 435 · 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 12. When one number is taken away, the average of the rest is 7. Which number was taken away? (a) 25 (b) 12 (c) 32 (d) 19
  2. 2.What is the average of all the whole numbers from 18 to 24? (a) 3 (b) 22 (c) 6 (d) 21
  3. 3.What is the average of all the whole numbers from 58 to 84? (a) 26 (b) 13 (c) 71 (d) 72
  4. 4.A batter has an average of 40 runs in 3 matches. How many runs are needed in the next match to raise the average to 48? (a) 48 (b) 56 (c) 32 (d) 72
  5. 5.A batter has an average of 60 runs in 5 matches. How many runs are needed in the next match to raise the average to 67? (a) 102 (b) 74 (c) 42 (d) 67
  6. 6.The average of 4 numbers is 21. When one number is taken away, the average of the rest is 22. Which number was taken away? (a) 18 (b) 19 (c) 43 (d) 21
  7. 7.A batter has an average of 27 runs in 6 matches. How many runs are needed in the next match to raise the average to 29? (a) 31 (b) 29 (c) 14 (d) 41
  8. 8.What is the average of 29, 33, 48, 24 and 41? (a) 37 (b) 34 (c) 36 (d) 35
  9. 9.What is the average of 49, 28, 37 and 30? (a) 37 (b) 48 (c) 35 (d) 36
  10. 10.A batter has an average of 58 runs in 3 matches. How many runs are needed in the next match to raise the average to 66? (a) 74 (b) 66 (c) 32 (d) 90
  11. 11.A batter has an average of 39 runs in 9 matches. How many runs are needed in the next match to raise the average to 42? (a) 30 (b) 45 (c) 69 (d) 42
  12. 12.What is the average of 8, 7, 23 and 46? (a) 22 (b) 28 (c) 20 (d) 21
  13. 13.What is the average of all the whole numbers from 45 to 59? (a) 52 (b) 14 (c) 53 (d) 7
  14. 14.A batter has an average of 32 runs in 3 matches. How many runs are needed in the next match to raise the average to 35? (a) 12 (b) 44 (c) 38 (d) 35
  15. 15.The average of 7 numbers is 29. When one number is taken away, the average of the rest is 28. Which number was taken away? (a) 35 (b) 29 (c) 57 (d) 7
  16. 16.What is the average of 49, 54, 61, 67, 56 and 97? (a) 66 (b) 63 (c) 64 (d) 65
  17. 17.A batter has an average of 27 runs in 4 matches. How many runs are needed in the next match to raise the average to 29? (a) 10 (b) 37 (c) 29 (d) 31
  18. 18.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) 37 (d) 32
  19. 19.A batter has an average of 53 runs in 4 matches. How many runs are needed in the next match to raise the average to 61? (a) 40 (b) 69 (c) 93 (d) 61
  20. 20.A batter has an average of 43 runs in 6 matches. How many runs are needed in the next match to raise the average to 45? (a) 45 (b) 47 (c) 57 (d) 14
  21. 21.The average of 8 numbers is 46. When one number is taken away, the average of the rest is 44. Which number was taken away? (a) 16 (b) 60 (c) 46 (d) 90
  22. 22.A batter has an average of 25 runs in 5 matches. How many runs are needed in the next match to raise the average to 33? (a) 41 (b) 33 (c) 48 (d) 73
  23. 23.What is the average of 26, 43, 51, 42 and 18? (a) 45 (b) 37 (c) 35 (d) 36
  24. 24.What is the average of 80, 84, 74, 65, 86 and 61? (a) 90 (b) 76 (c) 75 (d) 74
  25. 25.What is the average of all the whole numbers from 7 to 29? (a) 22 (b) 11 (c) 18 (d) 19
  26. 26.The average of 5 numbers is 29. When one number is taken away, the average of the rest is 30. Which number was taken away? (a) 26 (b) 25 (c) 59 (d) 29
  27. 27.A batter has an average of 59 runs in 6 matches. How many runs are needed in the next match to raise the average to 66? (a) 49 (b) 73 (c) 108 (d) 66
  28. 28.The average of 6 numbers is 35. When one number is taken away, the average of the rest is 30. Which number was taken away? (a) 60 (b) 35 (c) 30 (d) 65
  29. 29.A batter has an average of 45 runs in 8 matches. How many runs are needed in the next match to raise the average to 48? (a) 72 (b) 48 (c) 27 (d) 51
  30. 30.What is the average of 53, 74, 53, 64, 66 and 50? (a) 59 (b) 61 (c) 60 (d) 72
  31. 31.The average of 5 numbers is 44. When one number is taken away, the average of the rest is 40. Which number was taken away? (a) 84 (b) 44 (c) 60 (d) 20
  32. 32.The average of 4 numbers is 50. When one number is taken away, the average of the rest is 45. Which number was taken away? (a) 50 (b) 20 (c) 95 (d) 65
  33. 33.What is the average of 55, 57, 51 and 41? (a) 52 (b) 68 (c) 51 (d) 50
  34. 34.What is the average of 86, 60, 82, 78, 87 and 39? (a) 72 (b) 73 (c) 74 (d) 71
  35. 35.The average of 5 numbers is 21. When one number is taken away, the average of the rest is 18. Which number was taken away? (a) 33 (b) 39 (c) 15 (d) 21
  36. 36.The average of 4 numbers is 44. When one number is taken away, the average of the rest is 42. Which number was taken away? (a) 44 (b) 8 (c) 50 (d) 86
  37. 37.The average of 5 numbers is 26. When one number is taken away, the average of the rest is 27. Which number was taken away? (a) 26 (b) 23 (c) 53 (d) 22
  38. 38.A batter has an average of 29 runs in 4 matches. How many runs are needed in the next match to raise the average to 37? (a) 45 (b) 69 (c) 40 (d) 37
  39. 39.What is the average of 20, 15, 14 and 39? (a) 22 (b) 24 (c) 23 (d) 21
  40. 40.What is the average of 50, 51, 35, 43, 58 and 57? (a) 50 (b) 48 (c) 51 (d) 49

Answer key

  1. 32
  2. 21
  3. 71
  4. 72
  5. 102
  6. 18
  7. 41
  8. 35
  9. 36
  10. 90
  11. 69
  12. 21
  13. 52
  14. 44
  15. 35
  16. 64
  17. 37
  18. 31
  19. 93
  20. 57
  21. 60
  22. 73
  23. 36
  24. 75
  25. 18
  26. 25
  27. 108
  28. 60
  29. 72
  30. 60
  31. 60
  32. 65
  33. 51
  34. 72
  35. 33
  36. 50
  37. 22
  38. 69
  39. 22
  40. 49

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