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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 820 · 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 4 numbers is 18. When one number is taken away, the average of the rest is 17. Which number was taken away? (a) 21 (b) 4 (c) 18 (d) 35
  2. 2.What is the average of all the whole numbers from 32 to 60? (a) 46 (b) 14 (c) 28 (d) 47
  3. 3.A batter has an average of 23 runs in 6 matches. How many runs are needed in the next match to raise the average to 31? (a) 31 (b) 79 (c) 56 (d) 39
  4. 4.What is the average of all the whole numbers from 20 to 28? (a) 4 (b) 8 (c) 24 (d) 25
  5. 5.A batter has an average of 57 runs in 6 matches. How many runs are needed in the next match to raise the average to 64? (a) 106 (b) 71 (c) 49 (d) 64
  6. 6.What is the average of 45, 48, 37 and 14? (a) 36 (b) 48 (c) 35 (d) 37
  7. 7.What is the average of 30, 13, 10, 28, 22 and 41? (a) 25 (b) 23 (c) 26 (d) 24
  8. 8.What is the average of 23, 19, 28 and 14? (a) 20 (b) 28 (c) 22 (d) 21
  9. 9.The average of 6 numbers is 38. When one number is taken away, the average of the rest is 36. Which number was taken away? (a) 38 (b) 12 (c) 74 (d) 48
  10. 10.The average of 6 numbers is 11. When one number is taken away, the average of the rest is 10. Which number was taken away? (a) 11 (b) 6 (c) 21 (d) 16
  11. 11.What is the average of 87, 88, 88, 76 and 31? (a) 74 (b) 73 (c) 75 (d) 76
  12. 12.A batter has an average of 40 runs in 6 matches. How many runs are needed in the next match to raise the average to 43? (a) 46 (b) 21 (c) 61 (d) 43
  13. 13.The average of 5 numbers is 10. When one number is taken away, the average of the rest is 5. Which number was taken away? (a) 15 (b) 30 (c) 25 (d) 10
  14. 14.A batter has an average of 55 runs in 7 matches. How many runs are needed in the next match to raise the average to 58? (a) 58 (b) 79 (c) 24 (d) 61
  15. 15.What is the average of all the whole numbers from 20 to 44? (a) 24 (b) 32 (c) 12 (d) 33
  16. 16.What is the average of all the whole numbers from 33 to 41? (a) 8 (b) 4 (c) 38 (d) 37
  17. 17.What is the average of 46, 51, 38 and 69? (a) 68 (b) 51 (c) 50 (d) 52
  18. 18.A batter has an average of 57 runs in 9 matches. How many runs are needed in the next match to raise the average to 60? (a) 30 (b) 87 (c) 60 (d) 63
  19. 19.What is the average of 14, 40, 26 and 20? (a) 24 (b) 25 (c) 27 (d) 26
  20. 20.What is the average of all the whole numbers from 46 to 72? (a) 13 (b) 26 (c) 60 (d) 59
  21. 21.The average of 4 numbers is 33. When one number is taken away, the average of the rest is 32. Which number was taken away? (a) 33 (b) 4 (c) 36 (d) 65
  22. 22.A batter has an average of 57 runs in 5 matches. How many runs are needed in the next match to raise the average to 59? (a) 12 (b) 59 (c) 61 (d) 69
  23. 23.What is the average of all the whole numbers from 37 to 77? (a) 40 (b) 57 (c) 58 (d) 20
  24. 24.What is the average of 21, 31, 45, 19 and 49? (a) 32 (b) 34 (c) 33 (d) 35
  25. 25.What is the average of 37, 45, 39, 19 and 25? (a) 34 (b) 32 (c) 35 (d) 33
  26. 26.A batter has an average of 20 runs in 7 matches. How many runs are needed in the next match to raise the average to 27? (a) 56 (b) 34 (c) 76 (d) 27
  27. 27.The average of 6 numbers is 18. When one number is taken away, the average of the rest is 16. Which number was taken away? (a) 28 (b) 34 (c) 12 (d) 18
  28. 28.What is the average of all the whole numbers from 14 to 20? (a) 18 (b) 17 (c) 3 (d) 6
  29. 29.What is the average of 45, 25, 21 and 45? (a) 33 (b) 36 (c) 34 (d) 35
  30. 30.A batter has an average of 38 runs in 4 matches. How many runs are needed in the next match to raise the average to 44? (a) 30 (b) 44 (c) 50 (d) 68
  31. 31.What is the average of 64, 73, 75, 59, 67 and 46? (a) 64 (b) 65 (c) 66 (d) 63
  32. 32.What is the average of 10, 9, 17 and 60? (a) 24 (b) 23 (c) 32 (d) 25
  33. 33.What is the average of 74, 72, 83, 73 and 48? (a) 69 (b) 71 (c) 72 (d) 70
  34. 34.A batter has an average of 49 runs in 4 matches. How many runs are needed in the next match to raise the average to 57? (a) 65 (b) 40 (c) 89 (d) 57
  35. 35.A batter has an average of 59 runs in 5 matches. How many runs are needed in the next match to raise the average to 65? (a) 36 (b) 71 (c) 95 (d) 65
  36. 36.The average of 6 numbers is 30. When one number is taken away, the average of the rest is 27. Which number was taken away? (a) 30 (b) 57 (c) 45 (d) 18
  37. 37.What is the average of 25, 34, 34, 26 and 51? (a) 33 (b) 35 (c) 36 (d) 34
  38. 38.The average of 6 numbers is 41. When one number is taken away, the average of the rest is 38. Which number was taken away? (a) 56 (b) 41 (c) 79 (d) 18
  39. 39.What is the average of 86, 85, 72, 65, 67 and 69? (a) 75 (b) 74 (c) 73 (d) 76
  40. 40.The average of 4 numbers is 24. When one number is taken away, the average of the rest is 22. Which number was taken away? (a) 30 (b) 46 (c) 24 (d) 8

Answer key

  1. 21
  2. 46
  3. 79
  4. 24
  5. 106
  6. 36
  7. 24
  8. 21
  9. 48
  10. 16
  11. 74
  12. 61
  13. 30
  14. 79
  15. 32
  16. 37
  17. 51
  18. 87
  19. 25
  20. 59
  21. 36
  22. 69
  23. 57
  24. 33
  25. 33
  26. 76
  27. 28
  28. 17
  29. 34
  30. 68
  31. 64
  32. 24
  33. 70
  34. 89
  35. 95
  36. 45
  37. 34
  38. 56
  39. 74
  40. 30

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