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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 205 · 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 33, 14, 22 and 15? (a) 28 (b) 22 (c) 21 (d) 20
  2. 2.A batter has an average of 59 runs in 8 matches. How many runs are needed in the next match to raise the average to 61? (a) 18 (b) 77 (c) 61 (d) 63
  3. 3.The average of 8 numbers is 39. When one number is taken away, the average of the rest is 41. Which number was taken away? (a) 80 (b) 25 (c) 26 (d) 39
  4. 4.A batter has an average of 21 runs in 5 matches. How many runs are needed in the next match to raise the average to 27? (a) 57 (b) 33 (c) 36 (d) 27
  5. 5.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 61? (a) 69 (b) 63 (c) 10 (d) 61
  6. 6.The average of 8 numbers is 21. When one number is taken away, the average of the rest is 20. Which number was taken away? (a) 41 (b) 8 (c) 21 (d) 28
  7. 7.A batter has an average of 21 runs in 9 matches. How many runs are needed in the next match to raise the average to 28? (a) 70 (b) 91 (c) 28 (d) 35
  8. 8.The average of 6 numbers is 40. When one number is taken away, the average of the rest is 39. Which number was taken away? (a) 6 (b) 40 (c) 79 (d) 45
  9. 9.What is the average of 46, 57, 43, 40 and 69? (a) 53 (b) 50 (c) 51 (d) 52
  10. 10.What is the average of all the whole numbers from 40 to 76? (a) 18 (b) 36 (c) 59 (d) 58
  11. 11.The average of 6 numbers is 38. When one number is taken away, the average of the rest is 42. Which number was taken away? (a) 38 (b) 19 (c) 18 (d) 80
  12. 12.What is the average of 70, 50, 68, 61 and 61? (a) 61 (b) 62 (c) 64 (d) 63
  13. 13.What is the average of 49, 60, 67 and 68? (a) 60 (b) 63 (c) 61 (d) 62
  14. 14.What is the average of 50, 62, 75, 46 and 72? (a) 61 (b) 60 (c) 63 (d) 62
  15. 15.A batter has an average of 35 runs in 3 matches. How many runs are needed in the next match to raise the average to 38? (a) 12 (b) 41 (c) 47 (d) 38
  16. 16.A batter has an average of 47 runs in 3 matches. How many runs are needed in the next match to raise the average to 52? (a) 20 (b) 57 (c) 67 (d) 52
  17. 17.The average of 6 numbers is 38. When one number is taken away, the average of the rest is 37. Which number was taken away? (a) 75 (b) 6 (c) 43 (d) 38
  18. 18.The average of 6 numbers is 39. When one number is taken away, the average of the rest is 42. Which number was taken away? (a) 81 (b) 25 (c) 39 (d) 24
  19. 19.The average of 6 numbers is 14. When one number is taken away, the average of the rest is 10. Which number was taken away? (a) 35 (b) 24 (c) 34 (d) 14
  20. 20.What is the average of all the whole numbers from 53 to 91? (a) 38 (b) 19 (c) 73 (d) 72
  21. 21.What is the average of 85, 73, 78 and 48? (a) 70 (b) 72 (c) 71 (d) 73
  22. 22.What is the average of all the whole numbers from 53 to 61? (a) 4 (b) 57 (c) 8 (d) 58
  23. 23.The average of 4 numbers is 32. When one number is taken away, the average of the rest is 31. Which number was taken away? (a) 35 (b) 63 (c) 32 (d) 4
  24. 24.What is the average of 53, 56, 58, 55, 56 and 106? (a) 66 (b) 63 (c) 64 (d) 65
  25. 25.A batter has an average of 34 runs in 3 matches. How many runs are needed in the next match to raise the average to 39? (a) 20 (b) 44 (c) 39 (d) 54
  26. 26.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 27? (a) 18 (b) 29 (c) 27 (d) 43
  27. 27.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 31? (a) 31 (b) 37 (c) 67 (d) 42
  28. 28.A batter has an average of 30 runs in 9 matches. How many runs are needed in the next match to raise the average to 35? (a) 40 (b) 35 (c) 80 (d) 50
  29. 29.The average of 7 numbers is 10. When one number is taken away, the average of the rest is 7. Which number was taken away? (a) 17 (b) 10 (c) 21 (d) 28
  30. 30.What is the average of 34, 9, 19, 33, 10 and 33? (a) 22 (b) 25 (c) 23 (d) 24
  31. 31.A batter has an average of 54 runs in 4 matches. How many runs are needed in the next match to raise the average to 56? (a) 64 (b) 56 (c) 10 (d) 58
  32. 32.The average of 6 numbers is 21. When one number is taken away, the average of the rest is 22. Which number was taken away? (a) 43 (b) 17 (c) 21 (d) 16
  33. 33.A batter has an average of 46 runs in 7 matches. How many runs are needed in the next match to raise the average to 53? (a) 53 (b) 60 (c) 102 (d) 56
  34. 34.What is the average of 87, 73, 61, 87, 66 and 82? (a) 75 (b) 76 (c) 77 (d) 78
  35. 35.The average of 6 numbers is 32. When one number is taken away, the average of the rest is 28. Which number was taken away? (a) 60 (b) 32 (c) 24 (d) 52
  36. 36.The average of 7 numbers is 33. When one number is taken away, the average of the rest is 35. Which number was taken away? (a) 68 (b) 21 (c) 33 (d) 22
  37. 37.What is the average of 17, 19, 12 and 48? (a) 32 (b) 23 (c) 25 (d) 24
  38. 38.The average of 6 numbers is 18. When one number is taken away, the average of the rest is 14. Which number was taken away? (a) 18 (b) 32 (c) 24 (d) 38
  39. 39.What is the average of all the whole numbers from 55 to 77? (a) 67 (b) 11 (c) 66 (d) 22
  40. 40.What is the average of 36, 58, 60 and 26? (a) 60 (b) 46 (c) 44 (d) 45

Answer key

  1. 21
  2. 77
  3. 25
  4. 57
  5. 69
  6. 28
  7. 91
  8. 45
  9. 51
  10. 58
  11. 18
  12. 62
  13. 61
  14. 61
  15. 47
  16. 67
  17. 43
  18. 24
  19. 34
  20. 72
  21. 71
  22. 57
  23. 35
  24. 64
  25. 54
  26. 43
  27. 67
  28. 80
  29. 28
  30. 23
  31. 64
  32. 16
  33. 102
  34. 76
  35. 52
  36. 21
  37. 24
  38. 38
  39. 66
  40. 45

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