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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 493 · 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 32 runs in 7 matches. How many runs are needed in the next match to raise the average to 35? (a) 56 (b) 38 (c) 35 (d) 24
  2. 2.A batter has an average of 45 runs in 5 matches. How many runs are needed in the next match to raise the average to 49? (a) 53 (b) 49 (c) 24 (d) 69
  3. 3.The average of 5 numbers is 39. When one number is taken away, the average of the rest is 42. Which number was taken away? (a) 81 (b) 39 (c) 28 (d) 27
  4. 4.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 30? (a) 30 (b) 102 (c) 80 (d) 38
  5. 5.What is the average of 49, 62, 69 and 76? (a) 64 (b) 65 (c) 66 (d) 63
  6. 6.What is the average of 25, 39, 29, 12 and 15? (a) 25 (b) 24 (c) 23 (d) 30
  7. 7.What is the average of 50, 59, 47, 58 and 71? (a) 58 (b) 56 (c) 59 (d) 57
  8. 8.What is the average of all the whole numbers from 10 to 38? (a) 14 (b) 25 (c) 24 (d) 28
  9. 9.A batter has an average of 31 runs in 6 matches. How many runs are needed in the next match to raise the average to 37? (a) 43 (b) 37 (c) 42 (d) 73
  10. 10.A batter has an average of 36 runs in 8 matches. How many runs are needed in the next match to raise the average to 41? (a) 46 (b) 41 (c) 45 (d) 81
  11. 11.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 27? (a) 27 (b) 32 (c) 47 (d) 25
  12. 12.A batter has an average of 28 runs in 6 matches. How many runs are needed in the next match to raise the average to 30? (a) 30 (b) 32 (c) 42 (d) 14
  13. 13.The average of 5 numbers is 46. When one number is taken away, the average of the rest is 49. Which number was taken away? (a) 46 (b) 35 (c) 95 (d) 34
  14. 14.The average of 5 numbers is 12. When one number is taken away, the average of the rest is 11. Which number was taken away? (a) 23 (b) 16 (c) 5 (d) 12
  15. 15.What is the average of all the whole numbers from 59 to 73? (a) 14 (b) 7 (c) 67 (d) 66
  16. 16.The average of 7 numbers is 32. When one number is taken away, the average of the rest is 37. Which number was taken away? (a) 69 (b) 32 (c) 2 (d) 3
  17. 17.What is the average of 58, 54, 44, 56, 63 and 61? (a) 55 (b) 57 (c) 56 (d) 58
  18. 18.A batter has an average of 54 runs in 3 matches. How many runs are needed in the next match to raise the average to 59? (a) 64 (b) 74 (c) 20 (d) 59
  19. 19.What is the average of 56, 33, 53, 54 and 39? (a) 49 (b) 48 (c) 46 (d) 47
  20. 20.A batter has an average of 52 runs in 3 matches. How many runs are needed in the next match to raise the average to 60? (a) 68 (b) 60 (c) 32 (d) 84
  21. 21.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 58? (a) 58 (b) 66 (c) 72 (d) 122
  22. 22.The average of 5 numbers is 26. When one number is taken away, the average of the rest is 21. Which number was taken away? (a) 46 (b) 26 (c) 47 (d) 25
  23. 23.The average of 8 numbers is 32. When one number is taken away, the average of the rest is 31. Which number was taken away? (a) 63 (b) 8 (c) 39 (d) 32
  24. 24.The average of 8 numbers is 26. When one number is taken away, the average of the rest is 25. Which number was taken away? (a) 8 (b) 51 (c) 26 (d) 33
  25. 25.What is the average of 38, 42, 45, 34 and 41? (a) 39 (b) 50 (c) 41 (d) 40
  26. 26.The average of 8 numbers is 28. When one number is taken away, the average of the rest is 24. Which number was taken away? (a) 32 (b) 28 (c) 56 (d) 52
  27. 27.The average of 6 numbers is 39. When one number is taken away, the average of the rest is 44. Which number was taken away? (a) 83 (b) 14 (c) 15 (d) 39
  28. 28.The average of 4 numbers is 19. When one number is taken away, the average of the rest is 15. Which number was taken away? (a) 34 (b) 19 (c) 31 (d) 16
  29. 29.What is the average of 15, 19, 17 and 53? (a) 25 (b) 28 (c) 27 (d) 26
  30. 30.What is the average of 7, 28, 23 and 22? (a) 20 (b) 19 (c) 22 (d) 21
  31. 31.What is the average of all the whole numbers from 33 to 39? (a) 3 (b) 6 (c) 36 (d) 37
  32. 32.What is the average of all the whole numbers from 53 to 83? (a) 68 (b) 15 (c) 69 (d) 30
  33. 33.The average of 5 numbers is 30. When one number is taken away, the average of the rest is 27. Which number was taken away? (a) 42 (b) 30 (c) 15 (d) 57
  34. 34.What is the average of 54, 41, 56, 54, 36 and 53? (a) 51 (b) 49 (c) 50 (d) 48
  35. 35.The average of 5 numbers is 36. When one number is taken away, the average of the rest is 37. Which number was taken away? (a) 73 (b) 32 (c) 36 (d) 33
  36. 36.What is the average of all the whole numbers from 13 to 25? (a) 20 (b) 6 (c) 12 (d) 19
  37. 37.What is the average of 69, 65, 78 and 56? (a) 69 (b) 67 (c) 66 (d) 68
  38. 38.The average of 6 numbers is 17. When one number is taken away, the average of the rest is 15. Which number was taken away? (a) 27 (b) 12 (c) 32 (d) 17
  39. 39.What is the average of 55, 63, 37 and 37? (a) 64 (b) 47 (c) 48 (d) 49
  40. 40.What is the average of all the whole numbers from 36 to 52? (a) 45 (b) 16 (c) 44 (d) 8

Answer key

  1. 56
  2. 69
  3. 27
  4. 102
  5. 64
  6. 24
  7. 57
  8. 24
  9. 73
  10. 81
  11. 47
  12. 42
  13. 34
  14. 16
  15. 66
  16. 2
  17. 56
  18. 74
  19. 47
  20. 84
  21. 122
  22. 46
  23. 39
  24. 33
  25. 40
  26. 56
  27. 14
  28. 31
  29. 26
  30. 20
  31. 36
  32. 68
  33. 42
  34. 49
  35. 32
  36. 19
  37. 67
  38. 27
  39. 48
  40. 44

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