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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 153 · 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 8 numbers is 30. When one number is taken away, the average of the rest is 33. Which number was taken away? (a) 30 (b) 10 (c) 63 (d) 9
  2. 2.A batter has an average of 55 runs in 3 matches. How many runs are needed in the next match to raise the average to 59? (a) 71 (b) 63 (c) 16 (d) 59
  3. 3.The average of 7 numbers is 49. When one number is taken away, the average of the rest is 47. Which number was taken away? (a) 14 (b) 61 (c) 49 (d) 96
  4. 4.A batter has an average of 26 runs in 3 matches. How many runs are needed in the next match to raise the average to 31? (a) 20 (b) 46 (c) 36 (d) 31
  5. 5.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 36? (a) 36 (b) 16 (c) 40 (d) 48
  6. 6.The average of 7 numbers is 44. When one number is taken away, the average of the rest is 41. Which number was taken away? (a) 85 (b) 44 (c) 21 (d) 62
  7. 7.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) 14 (b) 57 (c) 47 (d) 45
  8. 8.What is the average of all the whole numbers from 54 to 84? (a) 70 (b) 15 (c) 69 (d) 30
  9. 9.The average of 8 numbers is 16. When one number is taken away, the average of the rest is 13. Which number was taken away? (a) 29 (b) 37 (c) 16 (d) 24
  10. 10.The average of 5 numbers is 36. When one number is taken away, the average of the rest is 32. Which number was taken away? (a) 68 (b) 36 (c) 52 (d) 20
  11. 11.What is the average of all the whole numbers from 9 to 33? (a) 24 (b) 21 (c) 22 (d) 12
  12. 12.A batter has an average of 41 runs in 8 matches. How many runs are needed in the next match to raise the average to 45? (a) 36 (b) 49 (c) 77 (d) 45
  13. 13.What is the average of 52, 42, 54, 32, 42 and 36? (a) 42 (b) 45 (c) 44 (d) 43
  14. 14.The average of 5 numbers is 16. When one number is taken away, the average of the rest is 19. Which number was taken away? (a) 4 (b) 35 (c) 5 (d) 16
  15. 15.What is the average of 33, 27, 43, 39 and 48? (a) 39 (b) 38 (c) 40 (d) 37
  16. 16.What is the average of 85, 67, 62 and 70? (a) 70 (b) 72 (c) 73 (d) 71
  17. 17.What is the average of 51, 60, 36, 44 and 54? (a) 48 (b) 51 (c) 49 (d) 50
  18. 18.What is the average of 36, 34, 55 and 59? (a) 48 (b) 46 (c) 47 (d) 45
  19. 19.The average of 4 numbers is 36. When one number is taken away, the average of the rest is 31. Which number was taken away? (a) 20 (b) 36 (c) 67 (d) 51
  20. 20.A batter has an average of 24 runs in 5 matches. How many runs are needed in the next match to raise the average to 30? (a) 36 (b) 61 (c) 60 (d) 30
  21. 21.What is the average of 73, 74, 78 and 39? (a) 67 (b) 66 (c) 88 (d) 65
  22. 22.A batter has an average of 26 runs in 4 matches. How many runs are needed in the next match to raise the average to 28? (a) 30 (b) 36 (c) 10 (d) 28
  23. 23.What is the average of all the whole numbers from 38 to 66? (a) 28 (b) 52 (c) 53 (d) 14
  24. 24.What is the average of 53, 44, 63, 40 and 65? (a) 54 (b) 53 (c) 55 (d) 52
  25. 25.The average of 4 numbers is 16. When one number is taken away, the average of the rest is 21. Which number was taken away? (a) 2 (b) 37 (c) 16 (d) 1
  26. 26.A batter has an average of 59 runs in 5 matches. How many runs are needed in the next match to raise the average to 62? (a) 65 (b) 77 (c) 62 (d) 18
  27. 27.The average of 8 numbers is 44. When one number is taken away, the average of the rest is 49. Which number was taken away? (a) 44 (b) 9 (c) 93 (d) 10
  28. 28.What is the average of 44, 48, 43, 45 and 55? (a) 47 (b) 49 (c) 48 (d) 46
  29. 29.The average of 4 numbers is 26. When one number is taken away, the average of the rest is 29. Which number was taken away? (a) 26 (b) 17 (c) 55 (d) 18
  30. 30.What is the average of 52, 69, 63, 45, 47 and 54? (a) 66 (b) 56 (c) 55 (d) 54
  31. 31.What is the average of 29, 42, 17 and 28? (a) 31 (b) 28 (c) 29 (d) 30
  32. 32.What is the average of all the whole numbers from 15 to 53? (a) 34 (b) 19 (c) 35 (d) 38
  33. 33.A batter has an average of 22 runs in 9 matches. How many runs are needed in the next match to raise the average to 26? (a) 62 (b) 40 (c) 26 (d) 30
  34. 34.The average of 6 numbers is 30. When one number is taken away, the average of the rest is 32. Which number was taken away? (a) 62 (b) 20 (c) 21 (d) 30
  35. 35.The average of 6 numbers is 16. When one number is taken away, the average of the rest is 17. Which number was taken away? (a) 12 (b) 16 (c) 33 (d) 11
  36. 36.A batter has an average of 53 runs in 9 matches. How many runs are needed in the next match to raise the average to 59? (a) 113 (b) 60 (c) 59 (d) 65
  37. 37.The average of 5 numbers is 18. When one number is taken away, the average of the rest is 21. Which number was taken away? (a) 18 (b) 7 (c) 6 (d) 39
  38. 38.The average of 6 numbers is 38. When one number is taken away, the average of the rest is 42. Which number was taken away? (a) 19 (b) 80 (c) 18 (d) 38
  39. 39.What is the average of 24, 28, 8, 35 and 5? (a) 20 (b) 21 (c) 25 (d) 19
  40. 40.What is the average of all the whole numbers from 42 to 50? (a) 46 (b) 47 (c) 4 (d) 8

Answer key

  1. 9
  2. 71
  3. 61
  4. 46
  5. 48
  6. 62
  7. 57
  8. 69
  9. 37
  10. 52
  11. 21
  12. 77
  13. 43
  14. 4
  15. 38
  16. 71
  17. 49
  18. 46
  19. 51
  20. 60
  21. 66
  22. 36
  23. 52
  24. 53
  25. 1
  26. 77
  27. 9
  28. 47
  29. 17
  30. 55
  31. 29
  32. 34
  33. 62
  34. 20
  35. 11
  36. 113
  37. 6
  38. 18
  39. 20
  40. 46

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