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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 419 · 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 7 numbers is 49. When one number is taken away, the average of the rest is 50. Which number was taken away? (a) 49 (b) 44 (c) 99 (d) 43
  2. 2.What is the average of 35, 18, 13 and 30? (a) 23 (b) 25 (c) 24 (d) 32
  3. 3.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) 28 (b) 51 (c) 72 (d) 58
  4. 4.A batter has an average of 40 runs in 9 matches. How many runs are needed in the next match to raise the average to 45? (a) 45 (b) 90 (c) 50 (d) 91
  5. 5.What is the average of 56, 83, 74, 77, 78 and 52? (a) 84 (b) 71 (c) 70 (d) 69
  6. 6.The average of 4 numbers is 16. When one number is taken away, the average of the rest is 14. Which number was taken away? (a) 22 (b) 8 (c) 30 (d) 16
  7. 7.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 24? (a) 26 (b) 24 (c) 10 (d) 32
  8. 8.The average of 4 numbers is 20. When one number is taken away, the average of the rest is 23. Which number was taken away? (a) 12 (b) 11 (c) 20 (d) 43
  9. 9.A batter has an average of 34 runs in 5 matches. How many runs are needed in the next match to raise the average to 42? (a) 48 (b) 42 (c) 50 (d) 82
  10. 10.What is the average of all the whole numbers from 18 to 42? (a) 31 (b) 24 (c) 12 (d) 30
  11. 11.What is the average of 26, 16, 35 and 31? (a) 26 (b) 27 (c) 36 (d) 28
  12. 12.What is the average of all the whole numbers from 34 to 58? (a) 47 (b) 24 (c) 12 (d) 46
  13. 13.A batter has an average of 25 runs in 6 matches. How many runs are needed in the next match to raise the average to 30? (a) 30 (b) 61 (c) 60 (d) 35
  14. 14.What is the average of 49, 42, 64 and 61? (a) 53 (b) 72 (c) 55 (d) 54
  15. 15.What is the average of 40, 13, 30 and 29? (a) 29 (b) 28 (c) 30 (d) 27
  16. 16.What is the average of all the whole numbers from 57 to 87? (a) 15 (b) 72 (c) 73 (d) 30
  17. 17.What is the average of 45, 47, 40 and 40? (a) 43 (b) 45 (c) 42 (d) 44
  18. 18.The average of 4 numbers is 49. When one number is taken away, the average of the rest is 54. Which number was taken away? (a) 34 (b) 103 (c) 35 (d) 49
  19. 19.What is the average of all the whole numbers from 37 to 59? (a) 22 (b) 49 (c) 48 (d) 11
  20. 20.What is the average of 53, 76, 76, 75 and 40? (a) 80 (b) 64 (c) 63 (d) 65
  21. 21.What is the average of 64, 55, 65 and 28? (a) 52 (b) 53 (c) 55 (d) 54
  22. 22.What is the average of 52, 56, 50, 58 and 14? (a) 48 (b) 45 (c) 46 (d) 47
  23. 23.A batter has an average of 50 runs in 8 matches. How many runs are needed in the next match to raise the average to 55? (a) 95 (b) 60 (c) 45 (d) 55
  24. 24.What is the average of 49, 72, 63, 73 and 38? (a) 61 (b) 60 (c) 59 (d) 58
  25. 25.What is the average of 77, 65, 69 and 101? (a) 77 (b) 78 (c) 104 (d) 79
  26. 26.The average of 4 numbers is 39. When one number is taken away, the average of the rest is 38. Which number was taken away? (a) 4 (b) 77 (c) 39 (d) 42
  27. 27.The average of 4 numbers is 40. When one number is taken away, the average of the rest is 39. Which number was taken away? (a) 40 (b) 79 (c) 4 (d) 43
  28. 28.The average of 4 numbers is 30. When one number is taken away, the average of the rest is 29. Which number was taken away? (a) 4 (b) 30 (c) 59 (d) 33
  29. 29.What is the average of 52, 35, 49, 53, 36 and 57? (a) 49 (b) 48 (c) 47 (d) 46
  30. 30.A batter has an average of 34 runs in 8 matches. How many runs are needed in the next match to raise the average to 40? (a) 88 (b) 40 (c) 46 (d) 54
  31. 31.A batter has an average of 36 runs in 3 matches. How many runs are needed in the next match to raise the average to 43? (a) 64 (b) 28 (c) 43 (d) 50
  32. 32.The average of 6 numbers is 50. When one number is taken away, the average of the rest is 55. Which number was taken away? (a) 26 (b) 105 (c) 25 (d) 50
  33. 33.A batter has an average of 29 runs in 7 matches. How many runs are needed in the next match to raise the average to 31? (a) 16 (b) 31 (c) 33 (d) 45
  34. 34.What is the average of all the whole numbers from 19 to 51? (a) 32 (b) 35 (c) 36 (d) 16
  35. 35.The average of 8 numbers is 38. When one number is taken away, the average of the rest is 37. Which number was taken away? (a) 38 (b) 8 (c) 75 (d) 45
  36. 36.What is the average of all the whole numbers from 58 to 98? (a) 40 (b) 79 (c) 78 (d) 20
  37. 37.The average of 7 numbers is 18. When one number is taken away, the average of the rest is 19. Which number was taken away? (a) 37 (b) 12 (c) 13 (d) 18
  38. 38.What is the average of all the whole numbers from 24 to 30? (a) 28 (b) 3 (c) 6 (d) 27
  39. 39.The average of 5 numbers is 43. When one number is taken away, the average of the rest is 41. Which number was taken away? (a) 10 (b) 51 (c) 84 (d) 43
  40. 40.The average of 6 numbers is 28. When one number is taken away, the average of the rest is 33. Which number was taken away? (a) 3 (b) 28 (c) 61 (d) 4

Answer key

  1. 43
  2. 24
  3. 72
  4. 90
  5. 70
  6. 22
  7. 32
  8. 11
  9. 82
  10. 30
  11. 27
  12. 46
  13. 60
  14. 54
  15. 28
  16. 72
  17. 43
  18. 34
  19. 48
  20. 64
  21. 53
  22. 46
  23. 95
  24. 59
  25. 78
  26. 42
  27. 43
  28. 33
  29. 47
  30. 88
  31. 64
  32. 25
  33. 45
  34. 35
  35. 45
  36. 78
  37. 12
  38. 27
  39. 51
  40. 3

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