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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 135 · 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 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
  2. 2.What is the average of 46, 40, 43, 54, 62 and 73? (a) 53 (b) 55 (c) 54 (d) 52
  3. 3.The average of 5 numbers is 46. When one number is taken away, the average of the rest is 43. Which number was taken away? (a) 46 (b) 89 (c) 58 (d) 15
  4. 4.The average of 8 numbers is 31. When one number is taken away, the average of the rest is 30. Which number was taken away? (a) 8 (b) 38 (c) 61 (d) 31
  5. 5.What is the average of all the whole numbers from 20 to 52? (a) 16 (b) 37 (c) 36 (d) 32
  6. 6.The average of 6 numbers is 23. When one number is taken away, the average of the rest is 24. Which number was taken away? (a) 18 (b) 47 (c) 23 (d) 19
  7. 7.What is the average of all the whole numbers from 51 to 81? (a) 15 (b) 30 (c) 66 (d) 67
  8. 8.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 28? (a) 32 (b) 40 (c) 28 (d) 16
  9. 9.What is the average of 43, 48, 41, 65 and 78? (a) 55 (b) 56 (c) 57 (d) 54
  10. 10.What is the average of all the whole numbers from 45 to 65? (a) 56 (b) 55 (c) 10 (d) 20
  11. 11.A batter has an average of 53 runs in 6 matches. How many runs are needed in the next match to raise the average to 61? (a) 109 (b) 69 (c) 56 (d) 61
  12. 12.The average of 5 numbers is 15. When one number is taken away, the average of the rest is 18. Which number was taken away? (a) 15 (b) 33 (c) 4 (d) 3
  13. 13.What is the average of all the whole numbers from 8 to 32? (a) 21 (b) 12 (c) 24 (d) 20
  14. 14.The average of 8 numbers is 40. When one number is taken away, the average of the rest is 45. Which number was taken away? (a) 40 (b) 85 (c) 5 (d) 6
  15. 15.The average of 7 numbers is 18. When one number is taken away, the average of the rest is 17. Which number was taken away? (a) 35 (b) 24 (c) 18 (d) 7
  16. 16.What is the average of 55, 62, 74 and 85? (a) 68 (b) 92 (c) 70 (d) 69
  17. 17.The average of 4 numbers is 25. When one number is taken away, the average of the rest is 29. Which number was taken away? (a) 54 (b) 25 (c) 14 (d) 13
  18. 18.The average of 5 numbers is 28. When one number is taken away, the average of the rest is 31. Which number was taken away? (a) 17 (b) 16 (c) 59 (d) 28
  19. 19.What is the average of all the whole numbers from 56 to 92? (a) 75 (b) 74 (c) 18 (d) 36
  20. 20.What is the average of 20, 18, 17, 16, 20 and 89? (a) 36 (b) 29 (c) 30 (d) 31
  21. 21.The average of 5 numbers is 20. When one number is taken away, the average of the rest is 15. Which number was taken away? (a) 25 (b) 35 (c) 20 (d) 40
  22. 22.What is the average of all the whole numbers from 50 to 70? (a) 20 (b) 10 (c) 61 (d) 60
  23. 23.What is the average of 36, 34, 59, 49 and 62? (a) 49 (b) 60 (c) 48 (d) 47
  24. 24.The average of 8 numbers is 10. When one number is taken away, the average of the rest is 6. Which number was taken away? (a) 10 (b) 38 (c) 16 (d) 32
  25. 25.A batter has an average of 27 runs in 3 matches. How many runs are needed in the next match to raise the average to 29? (a) 31 (b) 29 (c) 8 (d) 35
  26. 26.What is the average of 58, 77, 64 and 65? (a) 65 (b) 67 (c) 66 (d) 88
  27. 27.The average of 6 numbers is 14. When one number is taken away, the average of the rest is 16. Which number was taken away? (a) 4 (b) 30 (c) 14 (d) 5
  28. 28.What is the average of 15, 31, 35, 12 and 17? (a) 21 (b) 22 (c) 24 (d) 23
  29. 29.What is the average of 48, 33, 39 and 56? (a) 46 (b) 44 (c) 43 (d) 45
  30. 30.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 44? (a) 80 (b) 48 (c) 40 (d) 44
  31. 31.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) 24 (b) 49 (c) 69 (d) 53
  32. 32.The average of 4 numbers is 33. When one number is taken away, the average of the rest is 29. Which number was taken away? (a) 62 (b) 16 (c) 45 (d) 33
  33. 33.The average of 4 numbers is 18. When one number is taken away, the average of the rest is 22. Which number was taken away? (a) 18 (b) 6 (c) 40 (d) 7
  34. 34.The average of 4 numbers is 44. When one number is taken away, the average of the rest is 39. Which number was taken away? (a) 59 (b) 20 (c) 44 (d) 83
  35. 35.What is the average of 78, 72, 77, 56 and 47? (a) 68 (b) 65 (c) 67 (d) 66
  36. 36.The average of 4 numbers is 25. When one number is taken away, the average of the rest is 24. Which number was taken away? (a) 49 (b) 28 (c) 4 (d) 25
  37. 37.A batter has an average of 25 runs in 8 matches. How many runs are needed in the next match to raise the average to 28? (a) 31 (b) 28 (c) 27 (d) 52
  38. 38.What is the average of 47, 45, 43, 59, 40 and 96? (a) 56 (b) 55 (c) 54 (d) 66
  39. 39.A batter has an average of 37 runs in 9 matches. How many runs are needed in the next match to raise the average to 41? (a) 45 (b) 40 (c) 41 (d) 77
  40. 40.What is the average of all the whole numbers from 41 to 73? (a) 58 (b) 57 (c) 16 (d) 32

Answer key

  1. 12
  2. 53
  3. 58
  4. 38
  5. 36
  6. 18
  7. 66
  8. 40
  9. 55
  10. 55
  11. 109
  12. 3
  13. 20
  14. 5
  15. 24
  16. 69
  17. 13
  18. 16
  19. 74
  20. 30
  21. 40
  22. 60
  23. 48
  24. 38
  25. 35
  26. 66
  27. 4
  28. 22
  29. 44
  30. 80
  31. 69
  32. 45
  33. 6
  34. 59
  35. 66
  36. 28
  37. 52
  38. 55
  39. 77
  40. 57

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