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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 473 · 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 37. When one number is taken away, the average of the rest is 32. Which number was taken away? (a) 37 (b) 25 (c) 69 (d) 57
  2. 2.What is the average of 22, 26, 47, 45 and 35? (a) 35 (b) 37 (c) 34 (d) 36
  3. 3.What is the average of all the whole numbers from 31 to 71? (a) 51 (b) 20 (c) 52 (d) 40
  4. 4.What is the average of all the whole numbers from 31 to 41? (a) 10 (b) 37 (c) 36 (d) 5
  5. 5.What is the average of all the whole numbers from 11 to 47? (a) 36 (b) 18 (c) 29 (d) 30
  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 48? (a) 12 (b) 50 (c) 58 (d) 48
  7. 7.What is the average of all the whole numbers from 20 to 34? (a) 7 (b) 14 (c) 27 (d) 28
  8. 8.The average of 5 numbers is 34. When one number is taken away, the average of the rest is 33. Which number was taken away? (a) 38 (b) 67 (c) 34 (d) 5
  9. 9.What is the average of all the whole numbers from 18 to 28? (a) 24 (b) 10 (c) 5 (d) 23
  10. 10.The average of 5 numbers is 21. When one number is taken away, the average of the rest is 17. Which number was taken away? (a) 20 (b) 38 (c) 37 (d) 21
  11. 11.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) 24 (b) 73 (c) 57 (d) 53
  12. 12.The average of 8 numbers is 28. When one number is taken away, the average of the rest is 30. Which number was taken away? (a) 14 (b) 58 (c) 28 (d) 15
  13. 13.The average of 6 numbers is 36. When one number is taken away, the average of the rest is 34. Which number was taken away? (a) 70 (b) 46 (c) 36 (d) 12
  14. 14.What is the average of 35, 19, 22 and 40? (a) 31 (b) 28 (c) 30 (d) 29
  15. 15.What is the average of all the whole numbers from 37 to 47? (a) 42 (b) 10 (c) 5 (d) 43
  16. 16.What is the average of all the whole numbers from 12 to 32? (a) 22 (b) 20 (c) 23 (d) 10
  17. 17.A batter has an average of 29 runs in 9 matches. How many runs are needed in the next match to raise the average to 32? (a) 32 (b) 59 (c) 30 (d) 35
  18. 18.A batter has an average of 38 runs in 7 matches. How many runs are needed in the next match to raise the average to 46? (a) 64 (b) 54 (c) 102 (d) 46
  19. 19.The average of 7 numbers is 32. When one number is taken away, the average of the rest is 36. Which number was taken away? (a) 68 (b) 8 (c) 9 (d) 32
  20. 20.The average of 4 numbers is 13. When one number is taken away, the average of the rest is 10. Which number was taken away? (a) 22 (b) 12 (c) 23 (d) 13
  21. 21.What is the average of 62, 63, 51, 39, 41 and 32? (a) 48 (b) 49 (c) 47 (d) 50
  22. 22.What is the average of 53, 77, 80, 73, 65 and 42? (a) 66 (b) 78 (c) 64 (d) 65
  23. 23.The average of 5 numbers is 12. When one number is taken away, the average of the rest is 7. Which number was taken away? (a) 19 (b) 12 (c) 25 (d) 32
  24. 24.What is the average of all the whole numbers from 39 to 79? (a) 20 (b) 40 (c) 59 (d) 60
  25. 25.What is the average of 32, 29, 34, 30 and 60? (a) 38 (b) 37 (c) 39 (d) 36
  26. 26.A batter has an average of 57 runs in 7 matches. How many runs are needed in the next match to raise the average to 65? (a) 64 (b) 121 (c) 65 (d) 73
  27. 27.What is the average of all the whole numbers from 30 to 54? (a) 43 (b) 24 (c) 42 (d) 12
  28. 28.What is the average of 24, 10, 34, 25, 21 and 12? (a) 22 (b) 20 (c) 23 (d) 21
  29. 29.A batter has an average of 57 runs in 9 matches. How many runs are needed in the next match to raise the average to 62? (a) 62 (b) 67 (c) 50 (d) 107
  30. 30.What is the average of 27, 31, 23 and 71? (a) 37 (b) 40 (c) 38 (d) 39
  31. 31.What is the average of 40, 47, 49 and 36? (a) 44 (b) 45 (c) 43 (d) 42
  32. 32.The average of 5 numbers is 31. When one number is taken away, the average of the rest is 26. Which number was taken away? (a) 51 (b) 25 (c) 31 (d) 57
  33. 33.The average of 7 numbers is 38. When one number is taken away, the average of the rest is 37. Which number was taken away? (a) 38 (b) 7 (c) 44 (d) 75
  34. 34.What is the average of all the whole numbers from 34 to 74? (a) 55 (b) 54 (c) 40 (d) 20
  35. 35.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 56? (a) 61 (b) 101 (c) 50 (d) 56
  36. 36.What is the average of 50, 46, 64, 72 and 58? (a) 59 (b) 57 (c) 58 (d) 60
  37. 37.The average of 5 numbers is 13. When one number is taken away, the average of the rest is 8. Which number was taken away? (a) 33 (b) 13 (c) 25 (d) 21
  38. 38.The average of 4 numbers is 34. When one number is taken away, the average of the rest is 36. Which number was taken away? (a) 29 (b) 34 (c) 70 (d) 28
  39. 39.The average of 5 numbers is 44. When one number is taken away, the average of the rest is 45. Which number was taken away? (a) 89 (b) 40 (c) 44 (d) 41
  40. 40.The average of 6 numbers is 13. When one number is taken away, the average of the rest is 10. Which number was taken away? (a) 13 (b) 23 (c) 18 (d) 28

Answer key

  1. 57
  2. 35
  3. 51
  4. 36
  5. 29
  6. 58
  7. 27
  8. 38
  9. 23
  10. 37
  11. 73
  12. 14
  13. 46
  14. 29
  15. 42
  16. 22
  17. 59
  18. 102
  19. 8
  20. 22
  21. 48
  22. 65
  23. 32
  24. 59
  25. 37
  26. 121
  27. 42
  28. 21
  29. 107
  30. 38
  31. 43
  32. 51
  33. 44
  34. 54
  35. 101
  36. 58
  37. 33
  38. 28
  39. 40
  40. 28

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