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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 456 · 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 all the whole numbers from 53 to 89? (a) 72 (b) 18 (c) 36 (d) 71
  2. 2.The average of 8 numbers is 48. When one number is taken away, the average of the rest is 52. Which number was taken away? (a) 100 (b) 48 (c) 20 (d) 21
  3. 3.The average of 6 numbers is 32. When one number is taken away, the average of the rest is 34. Which number was taken away? (a) 32 (b) 23 (c) 22 (d) 66
  4. 4.A batter has an average of 22 runs in 4 matches. How many runs are needed in the next match to raise the average to 29? (a) 57 (b) 35 (c) 29 (d) 36
  5. 5.What is the average of all the whole numbers from 38 to 50? (a) 12 (b) 6 (c) 45 (d) 44
  6. 6.What is the average of 68, 61, 63 and 104? (a) 74 (b) 73 (c) 75 (d) 76
  7. 7.The average of 7 numbers is 40. When one number is taken away, the average of the rest is 38. Which number was taken away? (a) 14 (b) 40 (c) 78 (d) 52
  8. 8.What is the average of 40, 54, 42, 45, 28 and 31? (a) 48 (b) 41 (c) 39 (d) 40
  9. 9.A batter has an average of 43 runs in 6 matches. How many runs are needed in the next match to raise the average to 45? (a) 57 (b) 47 (c) 14 (d) 45
  10. 10.What is the average of 32, 9, 32 and 19? (a) 23 (b) 24 (c) 22 (d) 25
  11. 11.What is the average of 36, 59, 43, 38 and 64? (a) 48 (b) 60 (c) 49 (d) 47
  12. 12.A batter has an average of 43 runs in 4 matches. How many runs are needed in the next match to raise the average to 49? (a) 30 (b) 73 (c) 55 (d) 49
  13. 13.A batter has an average of 23 runs in 5 matches. How many runs are needed in the next match to raise the average to 27? (a) 31 (b) 27 (c) 24 (d) 47
  14. 14.A batter has an average of 33 runs in 8 matches. How many runs are needed in the next match to raise the average to 40? (a) 40 (b) 96 (c) 47 (d) 63
  15. 15.A batter has an average of 43 runs in 3 matches. How many runs are needed in the next match to raise the average to 48? (a) 48 (b) 63 (c) 53 (d) 20
  16. 16.What is the average of 31, 21, 22, 12 and 19? (a) 22 (b) 23 (c) 21 (d) 20
  17. 17.The average of 8 numbers is 31. When one number is taken away, the average of the rest is 27. Which number was taken away? (a) 59 (b) 58 (c) 32 (d) 31
  18. 18.The average of 6 numbers is 45. When one number is taken away, the average of the rest is 42. Which number was taken away? (a) 45 (b) 60 (c) 18 (d) 87
  19. 19.What is the average of 54, 55, 67 and 92? (a) 68 (b) 67 (c) 69 (d) 66
  20. 20.What is the average of 65, 45, 47, 53 and 60? (a) 53 (b) 54 (c) 55 (d) 56
  21. 21.What is the average of 29, 9, 18, 10 and 44? (a) 24 (b) 21 (c) 23 (d) 22
  22. 22.What is the average of 37, 17, 26, 34, 33 and 33? (a) 36 (b) 30 (c) 29 (d) 31
  23. 23.A batter has an average of 21 runs in 4 matches. How many runs are needed in the next match to raise the average to 29? (a) 40 (b) 61 (c) 37 (d) 29
  24. 24.The average of 7 numbers is 42. When one number is taken away, the average of the rest is 43. Which number was taken away? (a) 37 (b) 42 (c) 85 (d) 36
  25. 25.What is the average of 54, 57, 59, 40, 60 and 18? (a) 50 (b) 47 (c) 48 (d) 49
  26. 26.What is the average of 84, 84, 72 and 48? (a) 71 (b) 73 (c) 72 (d) 96
  27. 27.The average of 7 numbers is 27. When one number is taken away, the average of the rest is 23. Which number was taken away? (a) 51 (b) 28 (c) 50 (d) 27
  28. 28.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 49? (a) 91 (b) 48 (c) 55 (d) 49
  29. 29.What is the average of all the whole numbers from 36 to 74? (a) 19 (b) 55 (c) 38 (d) 56
  30. 30.The average of 5 numbers is 33. When one number is taken away, the average of the rest is 32. Which number was taken away? (a) 5 (b) 33 (c) 37 (d) 65
  31. 31.What is the average of all the whole numbers from 55 to 61? (a) 6 (b) 59 (c) 58 (d) 3
  32. 32.A batter has an average of 54 runs in 5 matches. How many runs are needed in the next match to raise the average to 58? (a) 62 (b) 78 (c) 58 (d) 24
  33. 33.The average of 6 numbers is 22. When one number is taken away, the average of the rest is 19. Which number was taken away? (a) 41 (b) 22 (c) 37 (d) 18
  34. 34.What is the average of all the whole numbers from 11 to 21? (a) 17 (b) 10 (c) 16 (d) 5
  35. 35.What is the average of 84, 68, 81, 64, 73 and 50? (a) 69 (b) 84 (c) 71 (d) 70
  36. 36.The average of 5 numbers is 16. When one number is taken away, the average of the rest is 13. Which number was taken away? (a) 29 (b) 28 (c) 16 (d) 15
  37. 37.What is the average of 69, 87, 79 and 81? (a) 80 (b) 79 (c) 78 (d) 81
  38. 38.The average of 4 numbers is 20. When one number is taken away, the average of the rest is 16. Which number was taken away? (a) 36 (b) 20 (c) 32 (d) 16
  39. 39.What is the average of 36, 47, 31 and 14? (a) 31 (b) 33 (c) 34 (d) 32
  40. 40.What is the average of 33, 34, 38 and 79? (a) 45 (b) 48 (c) 46 (d) 47

Answer key

  1. 71
  2. 20
  3. 22
  4. 57
  5. 44
  6. 74
  7. 52
  8. 40
  9. 57
  10. 23
  11. 48
  12. 73
  13. 47
  14. 96
  15. 63
  16. 21
  17. 59
  18. 60
  19. 67
  20. 54
  21. 22
  22. 30
  23. 61
  24. 36
  25. 48
  26. 72
  27. 51
  28. 91
  29. 55
  30. 37
  31. 58
  32. 78
  33. 37
  34. 16
  35. 70
  36. 28
  37. 79
  38. 32
  39. 32
  40. 46

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