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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 513 · 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 45. When one number is taken away, the average of the rest is 46. Which number was taken away? (a) 91 (b) 42 (c) 45 (d) 43
  2. 2.What is the average of 35, 12, 17, 18, 11 and 39? (a) 23 (b) 21 (c) 24 (d) 22
  3. 3.A batter has an average of 22 runs in 7 matches. How many runs are needed in the next match to raise the average to 30? (a) 38 (b) 30 (c) 64 (d) 86
  4. 4.The average of 7 numbers is 28. When one number is taken away, the average of the rest is 24. Which number was taken away? (a) 28 (b) 52 (c) 51 (d) 53
  5. 5.A batter has an average of 22 runs in 7 matches. How many runs are needed in the next match to raise the average to 29? (a) 78 (b) 36 (c) 56 (d) 29
  6. 6.A batter has an average of 40 runs in 7 matches. How many runs are needed in the next match to raise the average to 42? (a) 16 (b) 56 (c) 42 (d) 44
  7. 7.What is the average of 59, 43, 31, 32, 51 and 48? (a) 46 (b) 45 (c) 44 (d) 43
  8. 8.A batter has an average of 44 runs in 8 matches. How many runs are needed in the next match to raise the average to 52? (a) 116 (b) 60 (c) 52 (d) 72
  9. 9.What is the average of all the whole numbers from 15 to 23? (a) 4 (b) 8 (c) 19 (d) 20
  10. 10.The average of 4 numbers is 43. When one number is taken away, the average of the rest is 47. Which number was taken away? (a) 32 (b) 90 (c) 31 (d) 43
  11. 11.What is the average of 52, 36, 42, 57, 43 and 34? (a) 46 (b) 44 (c) 43 (d) 45
  12. 12.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 58? (a) 70 (b) 65 (c) 58 (d) 121
  13. 13.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 32? (a) 63 (b) 39 (c) 88 (d) 32
  14. 14.The average of 4 numbers is 34. When one number is taken away, the average of the rest is 35. Which number was taken away? (a) 34 (b) 31 (c) 69 (d) 32
  15. 15.The average of 8 numbers is 32. When one number is taken away, the average of the rest is 33. Which number was taken away? (a) 26 (b) 32 (c) 65 (d) 25
  16. 16.What is the average of 36, 30, 36 and 78? (a) 46 (b) 44 (c) 45 (d) 60
  17. 17.What is the average of all the whole numbers from 50 to 70? (a) 20 (b) 10 (c) 60 (d) 61
  18. 18.What is the average of 51, 53, 70 and 46? (a) 57 (b) 55 (c) 54 (d) 56
  19. 19.The average of 7 numbers is 46. When one number is taken away, the average of the rest is 50. Which number was taken away? (a) 96 (b) 46 (c) 22 (d) 23
  20. 20.What is the average of all the whole numbers from 35 to 55? (a) 45 (b) 46 (c) 10 (d) 20
  21. 21.A batter has an average of 49 runs in 5 matches. How many runs are needed in the next match to raise the average to 54? (a) 30 (b) 79 (c) 54 (d) 59
  22. 22.The average of 8 numbers is 38. When one number is taken away, the average of the rest is 39. Which number was taken away? (a) 31 (b) 32 (c) 77 (d) 38
  23. 23.What is the average of 59, 65, 74, 75, 53 and 70? (a) 67 (b) 65 (c) 66 (d) 68
  24. 24.The average of 4 numbers is 37. When one number is taken away, the average of the rest is 40. Which number was taken away? (a) 28 (b) 37 (c) 77 (d) 29
  25. 25.The average of 7 numbers is 25. When one number is taken away, the average of the rest is 23. Which number was taken away? (a) 48 (b) 14 (c) 25 (d) 37
  26. 26.What is the average of all the whole numbers from 11 to 21? (a) 16 (b) 10 (c) 5 (d) 17
  27. 27.A batter has an average of 60 runs in 7 matches. How many runs are needed in the next match to raise the average to 66? (a) 48 (b) 108 (c) 66 (d) 72
  28. 28.What is the average of 70, 94, 79 and 73? (a) 81 (b) 80 (c) 79 (d) 78
  29. 29.A batter has an average of 49 runs in 5 matches. How many runs are needed in the next match to raise the average to 53? (a) 57 (b) 53 (c) 24 (d) 73
  30. 30.The average of 5 numbers is 30. When one number is taken away, the average of the rest is 32. Which number was taken away? (a) 30 (b) 23 (c) 62 (d) 22
  31. 31.What is the average of all the whole numbers from 36 to 46? (a) 42 (b) 10 (c) 5 (d) 41
  32. 32.What is the average of all the whole numbers from 55 to 77? (a) 66 (b) 67 (c) 11 (d) 22
  33. 33.What is the average of all the whole numbers from 21 to 29? (a) 8 (b) 4 (c) 25 (d) 26
  34. 34.What is the average of 70, 79, 84, 65, 61 and 79? (a) 73 (b) 74 (c) 75 (d) 72
  35. 35.A batter has an average of 52 runs in 8 matches. How many runs are needed in the next match to raise the average to 56? (a) 56 (b) 60 (c) 88 (d) 36
  36. 36.What is the average of all the whole numbers from 8 to 24? (a) 17 (b) 15 (c) 8 (d) 16
  37. 37.What is the average of 38, 20, 9, 33, 20 and 24? (a) 25 (b) 24 (c) 23 (d) 26
  38. 38.The average of 4 numbers is 15. When one number is taken away, the average of the rest is 10. Which number was taken away? (a) 25 (b) 20 (c) 15 (d) 30
  39. 39.What is the average of all the whole numbers from 43 to 57? (a) 7 (b) 14 (c) 50 (d) 51
  40. 40.What is the average of 37, 35, 29, 30 and 34? (a) 33 (b) 35 (c) 34 (d) 32

Answer key

  1. 42
  2. 22
  3. 86
  4. 52
  5. 78
  6. 56
  7. 44
  8. 116
  9. 19
  10. 31
  11. 44
  12. 121
  13. 88
  14. 31
  15. 25
  16. 45
  17. 60
  18. 55
  19. 22
  20. 45
  21. 79
  22. 31
  23. 66
  24. 28
  25. 37
  26. 16
  27. 108
  28. 79
  29. 73
  30. 22
  31. 41
  32. 66
  33. 25
  34. 73
  35. 88
  36. 16
  37. 24
  38. 30
  39. 50
  40. 33

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