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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 499 · 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 17. When one number is taken away, the average of the rest is 15. Which number was taken away? (a) 17 (b) 32 (c) 25 (d) 10
  2. 2.A batter has an average of 30 runs in 3 matches. How many runs are needed in the next match to raise the average to 32? (a) 32 (b) 8 (c) 38 (d) 34
  3. 3.The average of 5 numbers is 30. When one number is taken away, the average of the rest is 26. Which number was taken away? (a) 46 (b) 30 (c) 20 (d) 56
  4. 4.What is the average of all the whole numbers from 8 to 36? (a) 14 (b) 28 (c) 23 (d) 22
  5. 5.The average of 7 numbers is 42. When one number is taken away, the average of the rest is 38. Which number was taken away? (a) 66 (b) 42 (c) 28 (d) 80
  6. 6.What is the average of all the whole numbers from 48 to 66? (a) 18 (b) 57 (c) 58 (d) 9
  7. 7.What is the average of 65, 66, 75, 76, 69 and 21? (a) 64 (b) 63 (c) 61 (d) 62
  8. 8.A batter has an average of 45 runs in 8 matches. How many runs are needed in the next match to raise the average to 53? (a) 72 (b) 53 (c) 117 (d) 61
  9. 9.What is the average of 60, 52, 35, 37, 36 and 80? (a) 60 (b) 49 (c) 50 (d) 51
  10. 10.What is the average of all the whole numbers from 23 to 33? (a) 10 (b) 5 (c) 29 (d) 28
  11. 11.The average of 4 numbers is 17. When one number is taken away, the average of the rest is 14. Which number was taken away? (a) 12 (b) 31 (c) 17 (d) 26
  12. 12.What is the average of 31, 7, 19, 9 and 39? (a) 22 (b) 23 (c) 20 (d) 21
  13. 13.What is the average of all the whole numbers from 15 to 37? (a) 22 (b) 27 (c) 11 (d) 26
  14. 14.A batter has an average of 59 runs in 4 matches. How many runs are needed in the next match to raise the average to 62? (a) 15 (b) 65 (c) 74 (d) 62
  15. 15.What is the average of 36, 34, 57, 51 and 67? (a) 51 (b) 48 (c) 49 (d) 50
  16. 16.What is the average of 78, 54, 68, 54, 72 and 76? (a) 68 (b) 69 (c) 67 (d) 66
  17. 17.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 47? (a) 51 (b) 32 (c) 47 (d) 75
  18. 18.The average of 4 numbers is 22. When one number is taken away, the average of the rest is 19. Which number was taken away? (a) 12 (b) 22 (c) 41 (d) 31
  19. 19.What is the average of all the whole numbers from 25 to 43? (a) 34 (b) 18 (c) 35 (d) 9
  20. 20.What is the average of 78, 56, 63, 82, 58 and 71? (a) 67 (b) 69 (c) 70 (d) 68
  21. 21.A batter has an average of 38 runs in 5 matches. How many runs are needed in the next match to raise the average to 42? (a) 24 (b) 46 (c) 42 (d) 62
  22. 22.What is the average of 52, 75, 53 and 80? (a) 66 (b) 64 (c) 65 (d) 67
  23. 23.The average of 4 numbers is 41. When one number is taken away, the average of the rest is 39. Which number was taken away? (a) 8 (b) 47 (c) 41 (d) 80
  24. 24.What is the average of all the whole numbers from 51 to 59? (a) 55 (b) 56 (c) 4 (d) 8
  25. 25.The average of 8 numbers is 11. When one number is taken away, the average of the rest is 6. Which number was taken away? (a) 11 (b) 40 (c) 46 (d) 17
  26. 26.What is the average of 55, 67, 77, 60, 62 and 51? (a) 64 (b) 63 (c) 61 (d) 62
  27. 27.A batter has an average of 46 runs in 8 matches. How many runs are needed in the next match to raise the average to 53? (a) 60 (b) 109 (c) 63 (d) 53
  28. 28.What is the average of 24, 32, 14 and 42? (a) 28 (b) 30 (c) 29 (d) 27
  29. 29.A batter has an average of 40 runs in 4 matches. How many runs are needed in the next match to raise the average to 47? (a) 35 (b) 75 (c) 47 (d) 54
  30. 30.A batter has an average of 58 runs in 4 matches. How many runs are needed in the next match to raise the average to 65? (a) 93 (b) 72 (c) 65 (d) 35
  31. 31.What is the average of 82, 60, 82, 59 and 52? (a) 67 (b) 69 (c) 68 (d) 66
  32. 32.The average of 8 numbers is 39. When one number is taken away, the average of the rest is 38. Which number was taken away? (a) 8 (b) 39 (c) 77 (d) 46
  33. 33.What is the average of all the whole numbers from 17 to 53? (a) 18 (b) 34 (c) 35 (d) 36
  34. 34.What is the average of 69, 68, 49, 44 and 55? (a) 57 (b) 58 (c) 56 (d) 59
  35. 35.A batter has an average of 34 runs in 8 matches. How many runs are needed in the next match to raise the average to 39? (a) 79 (b) 45 (c) 44 (d) 39
  36. 36.The average of 5 numbers is 16. When one number is taken away, the average of the rest is 11. Which number was taken away? (a) 27 (b) 16 (c) 36 (d) 25
  37. 37.A batter has an average of 25 runs in 6 matches. How many runs are needed in the next match to raise the average to 33? (a) 33 (b) 81 (c) 41 (d) 56
  38. 38.What is the average of all the whole numbers from 26 to 54? (a) 14 (b) 41 (c) 28 (d) 40
  39. 39.The average of 5 numbers is 32. When one number is taken away, the average of the rest is 36. Which number was taken away? (a) 32 (b) 16 (c) 68 (d) 17
  40. 40.What is the average of all the whole numbers from 48 to 56? (a) 52 (b) 53 (c) 8 (d) 4

Answer key

  1. 25
  2. 38
  3. 46
  4. 22
  5. 66
  6. 57
  7. 62
  8. 117
  9. 50
  10. 28
  11. 26
  12. 21
  13. 26
  14. 74
  15. 49
  16. 67
  17. 75
  18. 31
  19. 34
  20. 68
  21. 62
  22. 65
  23. 47
  24. 55
  25. 46
  26. 62
  27. 109
  28. 28
  29. 75
  30. 93
  31. 67
  32. 46
  33. 35
  34. 57
  35. 79
  36. 36
  37. 81
  38. 40
  39. 16
  40. 52

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