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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 446 · 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 37. When one number is taken away, the average of the rest is 35. Which number was taken away? (a) 37 (b) 45 (c) 10 (d) 72
  2. 2.A batter has an average of 38 runs in 7 matches. How many runs are needed in the next match to raise the average to 40? (a) 42 (b) 54 (c) 40 (d) 16
  3. 3.The average of 7 numbers is 42. When one number is taken away, the average of the rest is 46. Which number was taken away? (a) 88 (b) 19 (c) 42 (d) 18
  4. 4.A batter has an average of 30 runs in 3 matches. How many runs are needed in the next match to raise the average to 34? (a) 38 (b) 16 (c) 34 (d) 46
  5. 5.What is the average of 19, 42, 20, 20 and 54? (a) 32 (b) 30 (c) 31 (d) 33
  6. 6.What is the average of all the whole numbers from 16 to 48? (a) 32 (b) 16 (c) 31 (d) 33
  7. 7.The average of 7 numbers is 22. When one number is taken away, the average of the rest is 23. Which number was taken away? (a) 16 (b) 22 (c) 17 (d) 45
  8. 8.The average of 7 numbers is 48. When one number is taken away, the average of the rest is 51. Which number was taken away? (a) 30 (b) 99 (c) 31 (d) 48
  9. 9.The average of 4 numbers is 15. When one number is taken away, the average of the rest is 12. Which number was taken away? (a) 24 (b) 12 (c) 15 (d) 27
  10. 10.A batter has an average of 21 runs in 6 matches. How many runs are needed in the next match to raise the average to 28? (a) 35 (b) 28 (c) 70 (d) 49
  11. 11.What is the average of all the whole numbers from 29 to 65? (a) 18 (b) 48 (c) 36 (d) 47
  12. 12.What is the average of 68, 68, 45 and 59? (a) 80 (b) 60 (c) 61 (d) 59
  13. 13.What is the average of all the whole numbers from 32 to 64? (a) 16 (b) 48 (c) 32 (d) 49
  14. 14.The average of 6 numbers is 10. When one number is taken away, the average of the rest is 6. Which number was taken away? (a) 10 (b) 24 (c) 30 (d) 16
  15. 15.What is the average of 56, 65, 36, 42, 65 and 42? (a) 51 (b) 50 (c) 53 (d) 52
  16. 16.What is the average of all the whole numbers from 23 to 47? (a) 35 (b) 12 (c) 24 (d) 36
  17. 17.What is the average of all the whole numbers from 48 to 74? (a) 62 (b) 13 (c) 26 (d) 61
  18. 18.What is the average of 67, 75, 76, 65 and 97? (a) 77 (b) 95 (c) 75 (d) 76
  19. 19.A batter has an average of 56 runs in 7 matches. How many runs are needed in the next match to raise the average to 63? (a) 56 (b) 63 (c) 70 (d) 112
  20. 20.What is the average of 75, 77, 63 and 49? (a) 88 (b) 66 (c) 67 (d) 65
  21. 21.What is the average of 74, 80, 65, 82, 90 and 83? (a) 78 (b) 80 (c) 81 (d) 79
  22. 22.The average of 4 numbers is 47. When one number is taken away, the average of the rest is 42. Which number was taken away? (a) 89 (b) 62 (c) 20 (d) 47
  23. 23.What is the average of 47, 33, 51, 42 and 52? (a) 47 (b) 46 (c) 45 (d) 44
  24. 24.What is the average of all the whole numbers from 14 to 20? (a) 18 (b) 3 (c) 6 (d) 17
  25. 25.The average of 4 numbers is 24. When one number is taken away, the average of the rest is 19. Which number was taken away? (a) 24 (b) 20 (c) 43 (d) 39
  26. 26.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) 22 (b) 36 (c) 21 (d) 77
  27. 27.What is the average of 47, 54, 30 and 25? (a) 40 (b) 52 (c) 38 (d) 39
  28. 28.What is the average of all the whole numbers from 46 to 80? (a) 17 (b) 34 (c) 64 (d) 63
  29. 29.A batter has an average of 47 runs in 4 matches. How many runs are needed in the next match to raise the average to 53? (a) 30 (b) 77 (c) 59 (d) 53
  30. 30.The average of 6 numbers is 34. When one number is taken away, the average of the rest is 38. Which number was taken away? (a) 14 (b) 34 (c) 15 (d) 72
  31. 31.A batter has an average of 27 runs in 9 matches. How many runs are needed in the next match to raise the average to 29? (a) 29 (b) 31 (c) 47 (d) 20
  32. 32.The average of 7 numbers is 15. When one number is taken away, the average of the rest is 13. Which number was taken away? (a) 15 (b) 27 (c) 14 (d) 28
  33. 33.What is the average of 66, 68, 54, 59 and 18? (a) 53 (b) 55 (c) 52 (d) 54
  34. 34.The average of 7 numbers is 21. When one number is taken away, the average of the rest is 23. Which number was taken away? (a) 9 (b) 21 (c) 44 (d) 10
  35. 35.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 59? (a) 30 (b) 65 (c) 59 (d) 83
  36. 36.A batter has an average of 27 runs in 9 matches. How many runs are needed in the next match to raise the average to 34? (a) 41 (b) 97 (c) 70 (d) 34
  37. 37.The average of 4 numbers is 47. When one number is taken away, the average of the rest is 49. Which number was taken away? (a) 47 (b) 42 (c) 41 (d) 96
  38. 38.What is the average of 32, 35, 20 and 37? (a) 32 (b) 31 (c) 30 (d) 33
  39. 39.What is the average of all the whole numbers from 55 to 77? (a) 22 (b) 11 (c) 66 (d) 67
  40. 40.What is the average of all the whole numbers from 58 to 64? (a) 61 (b) 6 (c) 62 (d) 3

Answer key

  1. 45
  2. 54
  3. 18
  4. 46
  5. 31
  6. 32
  7. 16
  8. 30
  9. 24
  10. 70
  11. 47
  12. 60
  13. 48
  14. 30
  15. 51
  16. 35
  17. 61
  18. 76
  19. 112
  20. 66
  21. 79
  22. 62
  23. 45
  24. 17
  25. 39
  26. 21
  27. 39
  28. 63
  29. 77
  30. 14
  31. 47
  32. 27
  33. 53
  34. 9
  35. 83
  36. 97
  37. 41
  38. 31
  39. 66
  40. 61

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