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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 603 · 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 5 numbers is 32. When one number is taken away, the average of the rest is 29. Which number was taken away? (a) 15 (b) 32 (c) 61 (d) 44
  2. 2.What is the average of all the whole numbers from 12 to 18? (a) 16 (b) 6 (c) 3 (d) 15
  3. 3.A batter has an average of 23 runs in 8 matches. How many runs are needed in the next match to raise the average to 25? (a) 25 (b) 18 (c) 27 (d) 41
  4. 4.The average of 4 numbers is 14. When one number is taken away, the average of the rest is 16. Which number was taken away? (a) 30 (b) 14 (c) 8 (d) 9
  5. 5.What is the average of 65, 73, 72, 67, 63 and 32? (a) 63 (b) 64 (c) 61 (d) 62
  6. 6.A batter has an average of 46 runs in 5 matches. How many runs are needed in the next match to raise the average to 54? (a) 94 (b) 48 (c) 54 (d) 62
  7. 7.The average of 6 numbers is 25. When one number is taken away, the average of the rest is 21. Which number was taken away? (a) 25 (b) 46 (c) 24 (d) 45
  8. 8.The average of 4 numbers is 31. When one number is taken away, the average of the rest is 35. Which number was taken away? (a) 31 (b) 20 (c) 19 (d) 66
  9. 9.A batter has an average of 55 runs in 4 matches. How many runs are needed in the next match to raise the average to 58? (a) 70 (b) 15 (c) 61 (d) 58
  10. 10.A batter has an average of 23 runs in 3 matches. How many runs are needed in the next match to raise the average to 28? (a) 28 (b) 43 (c) 20 (d) 33
  11. 11.What is the average of 32, 32, 29 and 75? (a) 41 (b) 56 (c) 43 (d) 42
  12. 12.What is the average of 61, 66, 61, 65 and 112? (a) 75 (b) 72 (c) 73 (d) 74
  13. 13.What is the average of 57, 30, 52 and 29? (a) 41 (b) 43 (c) 42 (d) 56
  14. 14.What is the average of 43, 40, 30 and 35? (a) 38 (b) 37 (c) 39 (d) 36
  15. 15.A batter has an average of 21 runs in 5 matches. How many runs are needed in the next match to raise the average to 29? (a) 37 (b) 69 (c) 48 (d) 29
  16. 16.The average of 8 numbers is 46. When one number is taken away, the average of the rest is 50. Which number was taken away? (a) 96 (b) 19 (c) 18 (d) 46
  17. 17.A batter has an average of 54 runs in 7 matches. How many runs are needed in the next match to raise the average to 62? (a) 62 (b) 64 (c) 70 (d) 118
  18. 18.The average of 6 numbers is 20. When one number is taken away, the average of the rest is 23. Which number was taken away? (a) 6 (b) 20 (c) 5 (d) 43
  19. 19.What is the average of all the whole numbers from 20 to 60? (a) 40 (b) 41 (c) 39 (d) 20
  20. 20.The average of 6 numbers is 24. When one number is taken away, the average of the rest is 26. Which number was taken away? (a) 15 (b) 50 (c) 14 (d) 24
  21. 21.What is the average of all the whole numbers from 8 to 46? (a) 19 (b) 28 (c) 27 (d) 38
  22. 22.What is the average of all the whole numbers from 6 to 14? (a) 8 (b) 11 (c) 4 (d) 10
  23. 23.What is the average of 61, 69, 67, 63 and 20? (a) 57 (b) 55 (c) 70 (d) 56
  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 30? (a) 30 (b) 24 (c) 36 (d) 48
  25. 25.What is the average of all the whole numbers from 24 to 38? (a) 32 (b) 31 (c) 14 (d) 7
  26. 26.A batter has an average of 32 runs in 5 matches. How many runs are needed in the next match to raise the average to 36? (a) 36 (b) 56 (c) 40 (d) 24
  27. 27.A batter has an average of 55 runs in 6 matches. How many runs are needed in the next match to raise the average to 61? (a) 67 (b) 61 (c) 42 (d) 97
  28. 28.A batter has an average of 30 runs in 3 matches. How many runs are needed in the next match to raise the average to 33? (a) 42 (b) 36 (c) 12 (d) 33
  29. 29.The average of 8 numbers is 46. When one number is taken away, the average of the rest is 43. Which number was taken away? (a) 89 (b) 24 (c) 67 (d) 46
  30. 30.A batter has an average of 55 runs in 5 matches. How many runs are needed in the next match to raise the average to 60? (a) 65 (b) 85 (c) 30 (d) 60
  31. 31.What is the average of all the whole numbers from 29 to 57? (a) 43 (b) 44 (c) 28 (d) 14
  32. 32.What is the average of all the whole numbers from 31 to 55? (a) 24 (b) 12 (c) 44 (d) 43
  33. 33.What is the average of 43, 63, 53, 48 and 33? (a) 60 (b) 49 (c) 47 (d) 48
  34. 34.What is the average of 42, 16, 17, 30 and 45? (a) 31 (b) 29 (c) 30 (d) 32
  35. 35.What is the average of 77, 49, 51, 60 and 78? (a) 65 (b) 64 (c) 62 (d) 63
  36. 36.A batter has an average of 45 runs in 3 matches. How many runs are needed in the next match to raise the average to 47? (a) 49 (b) 53 (c) 8 (d) 47
  37. 37.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) 40 (b) 44 (c) 48 (d) 80
  38. 38.The average of 8 numbers is 48. When one number is taken away, the average of the rest is 44. Which number was taken away? (a) 92 (b) 76 (c) 32 (d) 48
  39. 39.What is the average of all the whole numbers from 14 to 22? (a) 8 (b) 19 (c) 4 (d) 18
  40. 40.What is the average of all the whole numbers from 9 to 17? (a) 14 (b) 8 (c) 13 (d) 4

Answer key

  1. 44
  2. 15
  3. 41
  4. 8
  5. 62
  6. 94
  7. 45
  8. 19
  9. 70
  10. 43
  11. 42
  12. 73
  13. 42
  14. 37
  15. 69
  16. 18
  17. 118
  18. 5
  19. 40
  20. 14
  21. 27
  22. 10
  23. 56
  24. 48
  25. 31
  26. 56
  27. 97
  28. 42
  29. 67
  30. 85
  31. 43
  32. 43
  33. 48
  34. 30
  35. 63
  36. 53
  37. 80
  38. 76
  39. 18
  40. 13

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