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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 172 · 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.A batter has an average of 41 runs in 6 matches. How many runs are needed in the next match to raise the average to 49? (a) 57 (b) 56 (c) 49 (d) 97
  2. 2.The average of 5 numbers is 37. When one number is taken away, the average of the rest is 36. Which number was taken away? (a) 41 (b) 73 (c) 37 (d) 5
  3. 3.What is the average of 44, 48, 63, 68 and 67? (a) 60 (b) 57 (c) 58 (d) 59
  4. 4.What is the average of 69, 49, 63, 52, 69 and 52? (a) 58 (b) 60 (c) 61 (d) 59
  5. 5.What is the average of all the whole numbers from 27 to 67? (a) 48 (b) 47 (c) 40 (d) 20
  6. 6.What is the average of 61, 63, 51, 69, 51 and 95? (a) 78 (b) 66 (c) 64 (d) 65
  7. 7.What is the average of all the whole numbers from 25 to 65? (a) 20 (b) 40 (c) 46 (d) 45
  8. 8.A batter has an average of 59 runs in 8 matches. How many runs are needed in the next match to raise the average to 61? (a) 63 (b) 61 (c) 18 (d) 77
  9. 9.What is the average of 79, 69, 79, 82, 72 and 81? (a) 77 (b) 79 (c) 76 (d) 78
  10. 10.A batter has an average of 26 runs in 8 matches. How many runs are needed in the next match to raise the average to 33? (a) 33 (b) 40 (c) 63 (d) 89
  11. 11.What is the average of all the whole numbers from 35 to 65? (a) 50 (b) 15 (c) 51 (d) 30
  12. 12.What is the average of all the whole numbers from 20 to 58? (a) 40 (b) 19 (c) 39 (d) 38
  13. 13.The average of 5 numbers is 45. When one number is taken away, the average of the rest is 49. Which number was taken away? (a) 94 (b) 30 (c) 45 (d) 29
  14. 14.What is the average of 51, 34, 62 and 49? (a) 49 (b) 51 (c) 48 (d) 50
  15. 15.The average of 7 numbers is 48. When one number is taken away, the average of the rest is 53. Which number was taken away? (a) 19 (b) 18 (c) 48 (d) 101
  16. 16.A batter has an average of 23 runs in 4 matches. How many runs are needed in the next match to raise the average to 25? (a) 33 (b) 10 (c) 27 (d) 25
  17. 17.A batter has an average of 34 runs in 9 matches. How many runs are needed in the next match to raise the average to 41? (a) 104 (b) 41 (c) 70 (d) 48
  18. 18.A batter has an average of 29 runs in 6 matches. How many runs are needed in the next match to raise the average to 37? (a) 45 (b) 56 (c) 37 (d) 85
  19. 19.The average of 4 numbers is 20. When one number is taken away, the average of the rest is 15. Which number was taken away? (a) 34 (b) 36 (c) 20 (d) 35
  20. 20.A batter has an average of 42 runs in 3 matches. How many runs are needed in the next match to raise the average to 47? (a) 52 (b) 47 (c) 62 (d) 20
  21. 21.The average of 4 numbers is 17. When one number is taken away, the average of the rest is 20. Which number was taken away? (a) 17 (b) 37 (c) 8 (d) 9
  22. 22.A batter has an average of 59 runs in 7 matches. How many runs are needed in the next match to raise the average to 67? (a) 75 (b) 123 (c) 64 (d) 67
  23. 23.The average of 8 numbers is 14. When one number is taken away, the average of the rest is 13. Which number was taken away? (a) 14 (b) 21 (c) 27 (d) 8
  24. 24.A batter has an average of 24 runs in 3 matches. How many runs are needed in the next match to raise the average to 26? (a) 26 (b) 8 (c) 28 (d) 32
  25. 25.What is the average of 42, 41, 18, 30, 17 and 44? (a) 34 (b) 31 (c) 32 (d) 33
  26. 26.What is the average of 55, 61, 53 and 71? (a) 60 (b) 80 (c) 59 (d) 61
  27. 27.The average of 4 numbers is 22. When one number is taken away, the average of the rest is 27. Which number was taken away? (a) 49 (b) 8 (c) 7 (d) 22
  28. 28.The average of 7 numbers is 24. When one number is taken away, the average of the rest is 26. Which number was taken away? (a) 13 (b) 24 (c) 50 (d) 12
  29. 29.The average of 6 numbers is 33. When one number is taken away, the average of the rest is 34. Which number was taken away? (a) 33 (b) 67 (c) 29 (d) 28
  30. 30.The average of 5 numbers is 36. When one number is taken away, the average of the rest is 39. Which number was taken away? (a) 75 (b) 24 (c) 25 (d) 36
  31. 31.What is the average of 56, 38, 58, 53 and 20? (a) 44 (b) 47 (c) 45 (d) 46
  32. 32.The average of 5 numbers is 49. When one number is taken away, the average of the rest is 52. Which number was taken away? (a) 37 (b) 101 (c) 38 (d) 49
  33. 33.A batter has an average of 22 runs in 5 matches. How many runs are needed in the next match to raise the average to 24? (a) 12 (b) 24 (c) 34 (d) 26
  34. 34.What is the average of 34, 24, 41 and 29? (a) 31 (b) 34 (c) 32 (d) 33
  35. 35.What is the average of 56, 43, 51, 71, 43 and 84? (a) 59 (b) 60 (c) 58 (d) 57
  36. 36.The average of 8 numbers is 12. When one number is taken away, the average of the rest is 8. Which number was taken away? (a) 40 (b) 12 (c) 32 (d) 20
  37. 37.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 53? (a) 80 (b) 61 (c) 125 (d) 53
  38. 38.The average of 6 numbers is 42. When one number is taken away, the average of the rest is 41. Which number was taken away? (a) 42 (b) 6 (c) 47 (d) 83
  39. 39.What is the average of 31, 51, 56 and 34? (a) 42 (b) 43 (c) 45 (d) 44
  40. 40.The average of 5 numbers is 22. When one number is taken away, the average of the rest is 25. Which number was taken away? (a) 10 (b) 11 (c) 22 (d) 47

Answer key

  1. 97
  2. 41
  3. 58
  4. 59
  5. 47
  6. 65
  7. 45
  8. 77
  9. 77
  10. 89
  11. 50
  12. 39
  13. 29
  14. 49
  15. 18
  16. 33
  17. 104
  18. 85
  19. 35
  20. 62
  21. 8
  22. 123
  23. 21
  24. 32
  25. 32
  26. 60
  27. 7
  28. 12
  29. 28
  30. 24
  31. 45
  32. 37
  33. 34
  34. 32
  35. 58
  36. 40
  37. 125
  38. 47
  39. 43
  40. 10

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