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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 370 · 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.What is the average of 68, 59, 46, 51, 64 and 30? (a) 55 (b) 52 (c) 53 (d) 54
  2. 2.What is the average of all the whole numbers from 10 to 32? (a) 22 (b) 21 (c) 20 (d) 11
  3. 3.A batter has an average of 27 runs in 9 matches. How many runs are needed in the next match to raise the average to 34? (a) 34 (b) 70 (c) 97 (d) 41
  4. 4.The average of 6 numbers is 33. When one number is taken away, the average of the rest is 32. Which number was taken away? (a) 6 (b) 33 (c) 65 (d) 38
  5. 5.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 39? (a) 27 (b) 42 (c) 63 (d) 39
  6. 6.A batter has an average of 51 runs in 9 matches. How many runs are needed in the next match to raise the average to 57? (a) 60 (b) 63 (c) 57 (d) 111
  7. 7.A batter has an average of 43 runs in 7 matches. How many runs are needed in the next match to raise the average to 45? (a) 16 (b) 59 (c) 47 (d) 45
  8. 8.What is the average of 73, 70, 53, 78 and 66? (a) 68 (b) 67 (c) 69 (d) 85
  9. 9.A batter has an average of 52 runs in 7 matches. How many runs are needed in the next match to raise the average to 59? (a) 56 (b) 59 (c) 108 (d) 66
  10. 10.What is the average of 26, 23, 31 and 44? (a) 30 (b) 32 (c) 33 (d) 31
  11. 11.The average of 4 numbers is 20. When one number is taken away, the average of the rest is 25. Which number was taken away? (a) 6 (b) 20 (c) 45 (d) 5
  12. 12.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) 44 (b) 83 (c) 20 (d) 59
  13. 13.The average of 5 numbers is 18. When one number is taken away, the average of the rest is 22. Which number was taken away? (a) 3 (b) 2 (c) 18 (d) 40
  14. 14.What is the average of 38, 37, 20 and 17? (a) 28 (b) 27 (c) 30 (d) 29
  15. 15.What is the average of all the whole numbers from 51 to 67? (a) 59 (b) 16 (c) 60 (d) 8
  16. 16.The average of 8 numbers is 40. When one number is taken away, the average of the rest is 37. Which number was taken away? (a) 61 (b) 40 (c) 77 (d) 24
  17. 17.What is the average of all the whole numbers from 54 to 88? (a) 71 (b) 34 (c) 17 (d) 72
  18. 18.What is the average of 27, 13, 11 and 29? (a) 19 (b) 22 (c) 21 (d) 20
  19. 19.What is the average of all the whole numbers from 41 to 71? (a) 57 (b) 56 (c) 15 (d) 30
  20. 20.What is the average of all the whole numbers from 48 to 84? (a) 66 (b) 18 (c) 36 (d) 67
  21. 21.What is the average of all the whole numbers from 20 to 36? (a) 8 (b) 28 (c) 29 (d) 16
  22. 22.What is the average of all the whole numbers from 24 to 60? (a) 36 (b) 42 (c) 43 (d) 18
  23. 23.What is the average of 53, 62, 76, 81, 75 and 61? (a) 67 (b) 69 (c) 70 (d) 68
  24. 24.The average of 7 numbers is 19. When one number is taken away, the average of the rest is 20. Which number was taken away? (a) 19 (b) 39 (c) 14 (d) 13
  25. 25.The average of 4 numbers is 32. When one number is taken away, the average of the rest is 31. Which number was taken away? (a) 63 (b) 35 (c) 4 (d) 32
  26. 26.What is the average of 87, 79, 72, 86, 70 and 44? (a) 75 (b) 73 (c) 74 (d) 72
  27. 27.What is the average of 42, 43, 27, 43, 22 and 45? (a) 36 (b) 37 (c) 38 (d) 39
  28. 28.A batter has an average of 32 runs in 6 matches. How many runs are needed in the next match to raise the average to 34? (a) 34 (b) 14 (c) 46 (d) 36
  29. 29.A batter has an average of 54 runs in 8 matches. How many runs are needed in the next match to raise the average to 60? (a) 108 (b) 60 (c) 66 (d) 54
  30. 30.The average of 7 numbers is 37. When one number is taken away, the average of the rest is 34. Which number was taken away? (a) 37 (b) 21 (c) 71 (d) 55
  31. 31.A batter has an average of 46 runs in 4 matches. How many runs are needed in the next match to raise the average to 52? (a) 30 (b) 58 (c) 76 (d) 52
  32. 32.What is the average of all the whole numbers from 42 to 76? (a) 17 (b) 60 (c) 59 (d) 34
  33. 33.What is the average of 72, 51, 56, 54 and 57? (a) 59 (b) 57 (c) 58 (d) 60
  34. 34.The average of 4 numbers is 34. When one number is taken away, the average of the rest is 31. Which number was taken away? (a) 43 (b) 12 (c) 65 (d) 34
  35. 35.What is the average of all the whole numbers from 56 to 66? (a) 61 (b) 62 (c) 5 (d) 10
  36. 36.What is the average of 66, 92, 66 and 84? (a) 76 (b) 79 (c) 78 (d) 77
  37. 37.What is the average of all the whole numbers from 7 to 13? (a) 6 (b) 11 (c) 3 (d) 10
  38. 38.What is the average of all the whole numbers from 53 to 75? (a) 64 (b) 22 (c) 11 (d) 65
  39. 39.The average of 7 numbers is 41. When one number is taken away, the average of the rest is 45. Which number was taken away? (a) 86 (b) 17 (c) 18 (d) 41
  40. 40.What is the average of all the whole numbers from 46 to 52? (a) 49 (b) 50 (c) 3 (d) 6

Answer key

  1. 53
  2. 21
  3. 97
  4. 38
  5. 63
  6. 111
  7. 59
  8. 68
  9. 108
  10. 31
  11. 5
  12. 59
  13. 2
  14. 28
  15. 59
  16. 61
  17. 71
  18. 20
  19. 56
  20. 66
  21. 28
  22. 42
  23. 68
  24. 13
  25. 35
  26. 73
  27. 37
  28. 46
  29. 108
  30. 55
  31. 76
  32. 59
  33. 58
  34. 43
  35. 61
  36. 77
  37. 10
  38. 64
  39. 17
  40. 49

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