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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 247 · 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 19. When one number is taken away, the average of the rest is 20. Which number was taken away? (a) 12 (b) 13 (c) 39 (d) 19
  2. 2.The average of 5 numbers is 24. When one number is taken away, the average of the rest is 25. Which number was taken away? (a) 20 (b) 21 (c) 49 (d) 24
  3. 3.What is the average of all the whole numbers from 14 to 26? (a) 12 (b) 20 (c) 21 (d) 6
  4. 4.A batter has an average of 35 runs in 5 matches. How many runs are needed in the next match to raise the average to 43? (a) 48 (b) 83 (c) 43 (d) 51
  5. 5.What is the average of all the whole numbers from 34 to 70? (a) 53 (b) 36 (c) 52 (d) 18
  6. 6.What is the average of 60, 76, 54, 76 and 79? (a) 69 (b) 71 (c) 70 (d) 68
  7. 7.What is the average of 29, 38, 34 and 11? (a) 27 (b) 28 (c) 30 (d) 29
  8. 8.What is the average of 24, 25, 32 and 43? (a) 32 (b) 30 (c) 33 (d) 31
  9. 9.What is the average of 61, 56, 66 and 81? (a) 66 (b) 88 (c) 67 (d) 65
  10. 10.The average of 5 numbers is 43. When one number is taken away, the average of the rest is 40. Which number was taken away? (a) 83 (b) 55 (c) 15 (d) 43
  11. 11.What is the average of 50, 42, 44 and 28? (a) 40 (b) 42 (c) 41 (d) 43
  12. 12.What is the average of all the whole numbers from 44 to 82? (a) 63 (b) 64 (c) 38 (d) 19
  13. 13.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 58? (a) 63 (b) 50 (c) 103 (d) 58
  14. 14.The average of 4 numbers is 31. When one number is taken away, the average of the rest is 28. Which number was taken away? (a) 40 (b) 12 (c) 59 (d) 31
  15. 15.What is the average of all the whole numbers from 40 to 72? (a) 32 (b) 57 (c) 56 (d) 16
  16. 16.What is the average of 59, 60, 61 and 96? (a) 92 (b) 70 (c) 69 (d) 68
  17. 17.A batter has an average of 30 runs in 5 matches. How many runs are needed in the next match to raise the average to 33? (a) 18 (b) 33 (c) 36 (d) 48
  18. 18.What is the average of 54, 60, 69 and 61? (a) 60 (b) 61 (c) 63 (d) 62
  19. 19.The average of 8 numbers is 14. When one number is taken away, the average of the rest is 10. Which number was taken away? (a) 24 (b) 32 (c) 42 (d) 14
  20. 20.The average of 8 numbers is 18. When one number is taken away, the average of the rest is 13. Which number was taken away? (a) 53 (b) 18 (c) 31 (d) 40
  21. 21.A batter has an average of 35 runs in 8 matches. How many runs are needed in the next match to raise the average to 40? (a) 40 (b) 45 (c) 80 (d) 81
  22. 22.The average of 7 numbers is 15. When one number is taken away, the average of the rest is 16. Which number was taken away? (a) 15 (b) 31 (c) 10 (d) 9
  23. 23.A batter has an average of 58 runs in 7 matches. How many runs are needed in the next match to raise the average to 64? (a) 64 (b) 48 (c) 106 (d) 70
  24. 24.What is the average of all the whole numbers from 40 to 52? (a) 47 (b) 6 (c) 46 (d) 12
  25. 25.The average of 6 numbers is 31. When one number is taken away, the average of the rest is 29. Which number was taken away? (a) 12 (b) 60 (c) 41 (d) 31
  26. 26.What is the average of 20, 37, 43, 42 and 13? (a) 31 (b) 32 (c) 33 (d) 30
  27. 27.A batter has an average of 48 runs in 7 matches. How many runs are needed in the next match to raise the average to 53? (a) 40 (b) 53 (c) 58 (d) 88
  28. 28.What is the average of 40, 34, 62 and 52? (a) 49 (b) 46 (c) 47 (d) 48
  29. 29.What is the average of 47, 46, 39 and 84? (a) 53 (b) 72 (c) 55 (d) 54
  30. 30.What is the average of 49, 45, 44 and 54? (a) 49 (b) 47 (c) 64 (d) 48
  31. 31.What is the average of 39, 37, 26, 42, 37 and 41? (a) 39 (b) 36 (c) 37 (d) 38
  32. 32.The average of 4 numbers is 12. When one number is taken away, the average of the rest is 10. Which number was taken away? (a) 8 (b) 22 (c) 18 (d) 12
  33. 33.What is the average of 64, 52, 60, 75 and 84? (a) 68 (b) 69 (c) 66 (d) 67
  34. 34.A batter has an average of 49 runs in 9 matches. How many runs are needed in the next match to raise the average to 57? (a) 65 (b) 129 (c) 80 (d) 57
  35. 35.A batter has an average of 50 runs in 9 matches. How many runs are needed in the next match to raise the average to 56? (a) 62 (b) 56 (c) 60 (d) 110
  36. 36.A batter has an average of 56 runs in 8 matches. How many runs are needed in the next match to raise the average to 60? (a) 36 (b) 92 (c) 60 (d) 64
  37. 37.What is the average of all the whole numbers from 56 to 74? (a) 18 (b) 9 (c) 65 (d) 66
  38. 38.What is the average of 44, 64, 41, 47, 62 and 66? (a) 55 (b) 53 (c) 56 (d) 54
  39. 39.What is the average of 78, 74, 64, 66 and 38? (a) 65 (b) 80 (c) 63 (d) 64
  40. 40.What is the average of all the whole numbers from 15 to 41? (a) 28 (b) 13 (c) 29 (d) 26

Answer key

  1. 12
  2. 20
  3. 20
  4. 83
  5. 52
  6. 69
  7. 28
  8. 31
  9. 66
  10. 55
  11. 41
  12. 63
  13. 103
  14. 40
  15. 56
  16. 69
  17. 48
  18. 61
  19. 42
  20. 53
  21. 80
  22. 9
  23. 106
  24. 46
  25. 41
  26. 31
  27. 88
  28. 47
  29. 54
  30. 48
  31. 37
  32. 18
  33. 67
  34. 129
  35. 110
  36. 92
  37. 65
  38. 54
  39. 64
  40. 28

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