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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 841 · 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.A batter has an average of 60 runs in 6 matches. How many runs are needed in the next match to raise the average to 67? (a) 74 (b) 49 (c) 109 (d) 67
  2. 2.A batter has an average of 47 runs in 9 matches. How many runs are needed in the next match to raise the average to 50? (a) 77 (b) 50 (c) 30 (d) 53
  3. 3.What is the average of all the whole numbers from 59 to 79? (a) 70 (b) 10 (c) 20 (d) 69
  4. 4.What is the average of 82, 72, 65 and 65? (a) 70 (b) 72 (c) 73 (d) 71
  5. 5.What is the average of all the whole numbers from 20 to 40? (a) 20 (b) 31 (c) 10 (d) 30
  6. 6.The average of 6 numbers is 16. When one number is taken away, the average of the rest is 18. Which number was taken away? (a) 34 (b) 16 (c) 7 (d) 6
  7. 7.A batter has an average of 59 runs in 7 matches. How many runs are needed in the next match to raise the average to 61? (a) 61 (b) 16 (c) 63 (d) 75
  8. 8.The average of 7 numbers is 11. When one number is taken away, the average of the rest is 12. Which number was taken away? (a) 11 (b) 6 (c) 23 (d) 5
  9. 9.What is the average of 53, 46, 39, 45, 63 and 42? (a) 50 (b) 48 (c) 49 (d) 47
  10. 10.A batter has an average of 53 runs in 4 matches. How many runs are needed in the next match to raise the average to 56? (a) 59 (b) 68 (c) 15 (d) 56
  11. 11.What is the average of 66, 61, 59 and 22? (a) 52 (b) 51 (c) 53 (d) 54
  12. 12.What is the average of all the whole numbers from 17 to 29? (a) 23 (b) 12 (c) 6 (d) 24
  13. 13.The average of 6 numbers is 31. When one number is taken away, the average of the rest is 32. Which number was taken away? (a) 63 (b) 31 (c) 26 (d) 27
  14. 14.The average of 4 numbers is 16. When one number is taken away, the average of the rest is 13. Which number was taken away? (a) 29 (b) 12 (c) 25 (d) 16
  15. 15.A batter has an average of 29 runs in 3 matches. How many runs are needed in the next match to raise the average to 33? (a) 33 (b) 16 (c) 45 (d) 37
  16. 16.The average of 4 numbers is 27. When one number is taken away, the average of the rest is 25. Which number was taken away? (a) 8 (b) 33 (c) 52 (d) 27
  17. 17.What is the average of 32, 33, 36, 25 and 59? (a) 38 (b) 37 (c) 36 (d) 39
  18. 18.The average of 4 numbers is 11. When one number is taken away, the average of the rest is 13. Which number was taken away? (a) 11 (b) 24 (c) 6 (d) 5
  19. 19.The average of 7 numbers is 18. When one number is taken away, the average of the rest is 16. Which number was taken away? (a) 34 (b) 30 (c) 18 (d) 14
  20. 20.What is the average of all the whole numbers from 18 to 46? (a) 28 (b) 32 (c) 14 (d) 33
  21. 21.The average of 5 numbers is 12. When one number is taken away, the average of the rest is 13. Which number was taken away? (a) 25 (b) 12 (c) 9 (d) 8
  22. 22.A batter has an average of 25 runs in 9 matches. How many runs are needed in the next match to raise the average to 33? (a) 33 (b) 80 (c) 41 (d) 105
  23. 23.The average of 8 numbers is 50. When one number is taken away, the average of the rest is 45. Which number was taken away? (a) 95 (b) 50 (c) 40 (d) 85
  24. 24.A batter has an average of 37 runs in 4 matches. How many runs are needed in the next match to raise the average to 44? (a) 51 (b) 35 (c) 72 (d) 44
  25. 25.What is the average of all the whole numbers from 56 to 70? (a) 64 (b) 7 (c) 14 (d) 63
  26. 26.A batter has an average of 26 runs in 8 matches. How many runs are needed in the next match to raise the average to 32? (a) 32 (b) 54 (c) 38 (d) 80
  27. 27.A batter has an average of 58 runs in 6 matches. How many runs are needed in the next match to raise the average to 61? (a) 21 (b) 79 (c) 64 (d) 61
  28. 28.What is the average of all the whole numbers from 54 to 86? (a) 70 (b) 16 (c) 32 (d) 71
  29. 29.A batter has an average of 51 runs in 3 matches. How many runs are needed in the next match to raise the average to 58? (a) 65 (b) 58 (c) 28 (d) 79
  30. 30.What is the average of 24, 13, 9 and 42? (a) 24 (b) 22 (c) 21 (d) 23
  31. 31.What is the average of 74, 60, 70, 66, 59 and 43? (a) 62 (b) 61 (c) 63 (d) 64
  32. 32.The average of 4 numbers is 18. When one number is taken away, the average of the rest is 20. Which number was taken away? (a) 38 (b) 12 (c) 18 (d) 13
  33. 33.What is the average of 33, 31, 36, 26, 49 and 71? (a) 41 (b) 42 (c) 43 (d) 40
  34. 34.What is the average of 28, 22, 12, 32 and 21? (a) 25 (b) 23 (c) 24 (d) 22
  35. 35.What is the average of 51, 54, 30, 38 and 22? (a) 39 (b) 40 (c) 38 (d) 41
  36. 36.The average of 5 numbers is 13. When one number is taken away, the average of the rest is 10. Which number was taken away? (a) 23 (b) 13 (c) 15 (d) 25
  37. 37.What is the average of all the whole numbers from 15 to 49? (a) 33 (b) 17 (c) 34 (d) 32
  38. 38.What is the average of all the whole numbers from 9 to 15? (a) 6 (b) 12 (c) 13 (d) 3
  39. 39.What is the average of all the whole numbers from 48 to 66? (a) 58 (b) 18 (c) 9 (d) 57
  40. 40.What is the average of all the whole numbers from 12 to 48? (a) 36 (b) 18 (c) 31 (d) 30

Answer key

  1. 109
  2. 77
  3. 69
  4. 71
  5. 30
  6. 6
  7. 75
  8. 5
  9. 48
  10. 68
  11. 52
  12. 23
  13. 26
  14. 25
  15. 45
  16. 33
  17. 37
  18. 5
  19. 30
  20. 32
  21. 8
  22. 105
  23. 85
  24. 72
  25. 63
  26. 80
  27. 79
  28. 70
  29. 79
  30. 22
  31. 62
  32. 12
  33. 41
  34. 23
  35. 39
  36. 25
  37. 32
  38. 12
  39. 57
  40. 30

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