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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 796 · 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 8 numbers is 18. When one number is taken away, the average of the rest is 15. Which number was taken away? (a) 33 (b) 24 (c) 39 (d) 18
  2. 2.The average of 6 numbers is 45. When one number is taken away, the average of the rest is 49. Which number was taken away? (a) 25 (b) 26 (c) 45 (d) 94
  3. 3.The average of 8 numbers is 40. When one number is taken away, the average of the rest is 39. Which number was taken away? (a) 8 (b) 40 (c) 47 (d) 79
  4. 4.A batter has an average of 39 runs in 3 matches. How many runs are needed in the next match to raise the average to 43? (a) 43 (b) 47 (c) 55 (d) 16
  5. 5.What is the average of 68, 67, 42, 67 and 41? (a) 58 (b) 56 (c) 59 (d) 57
  6. 6.A batter has an average of 55 runs in 8 matches. How many runs are needed in the next match to raise the average to 61? (a) 109 (b) 54 (c) 61 (d) 67
  7. 7.What is the average of 15, 32, 10 and 23? (a) 19 (b) 20 (c) 22 (d) 21
  8. 8.A batter has an average of 51 runs in 6 matches. How many runs are needed in the next match to raise the average to 54? (a) 57 (b) 54 (c) 21 (d) 72
  9. 9.What is the average of 16, 33, 21 and 34? (a) 27 (b) 25 (c) 28 (d) 26
  10. 10.The average of 8 numbers is 10. When one number is taken away, the average of the rest is 5. Which number was taken away? (a) 10 (b) 40 (c) 15 (d) 45
  11. 11.A batter has an average of 51 runs in 4 matches. How many runs are needed in the next match to raise the average to 54? (a) 57 (b) 15 (c) 66 (d) 54
  12. 12.What is the average of 16, 33, 25, 25, 31 and 8? (a) 23 (b) 25 (c) 22 (d) 24
  13. 13.A batter has an average of 51 runs in 5 matches. How many runs are needed in the next match to raise the average to 59? (a) 59 (b) 67 (c) 99 (d) 48
  14. 14.A batter has an average of 55 runs in 5 matches. How many runs are needed in the next match to raise the average to 63? (a) 63 (b) 103 (c) 48 (d) 71
  15. 15.What is the average of 8, 9, 30 and 33? (a) 21 (b) 19 (c) 22 (d) 20
  16. 16.The average of 7 numbers is 49. When one number is taken away, the average of the rest is 52. Which number was taken away? (a) 32 (b) 49 (c) 31 (d) 101
  17. 17.What is the average of 31, 21, 25, 13, 29 and 37? (a) 26 (b) 28 (c) 25 (d) 27
  18. 18.A batter has an average of 28 runs in 3 matches. How many runs are needed in the next match to raise the average to 32? (a) 36 (b) 16 (c) 44 (d) 32
  19. 19.The average of 6 numbers is 17. When one number is taken away, the average of the rest is 20. Which number was taken away? (a) 3 (b) 37 (c) 2 (d) 17
  20. 20.What is the average of 48, 31, 33 and 56? (a) 43 (b) 56 (c) 41 (d) 42
  21. 21.What is the average of all the whole numbers from 33 to 47? (a) 7 (b) 41 (c) 14 (d) 40
  22. 22.What is the average of all the whole numbers from 11 to 31? (a) 21 (b) 20 (c) 22 (d) 10
  23. 23.What is the average of 68, 60, 55 and 85? (a) 66 (b) 69 (c) 67 (d) 68
  24. 24.A batter has an average of 28 runs in 8 matches. How many runs are needed in the next match to raise the average to 31? (a) 27 (b) 34 (c) 55 (d) 31
  25. 25.What is the average of all the whole numbers from 16 to 42? (a) 13 (b) 26 (c) 29 (d) 30
  26. 26.What is the average of all the whole numbers from 39 to 69? (a) 15 (b) 54 (c) 30 (d) 55
  27. 27.A batter has an average of 41 runs in 3 matches. How many runs are needed in the next match to raise the average to 47? (a) 24 (b) 65 (c) 53 (d) 47
  28. 28.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 42? (a) 42 (b) 62 (c) 25 (d) 47
  29. 29.What is the average of all the whole numbers from 14 to 48? (a) 32 (b) 31 (c) 17 (d) 34
  30. 30.What is the average of all the whole numbers from 20 to 26? (a) 23 (b) 3 (c) 6 (d) 24
  31. 31.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 54? (a) 63 (b) 57 (c) 12 (d) 54
  32. 32.The average of 4 numbers is 35. When one number is taken away, the average of the rest is 39. Which number was taken away? (a) 24 (b) 74 (c) 35 (d) 23
  33. 33.The average of 5 numbers is 44. When one number is taken away, the average of the rest is 41. Which number was taken away? (a) 15 (b) 56 (c) 44 (d) 85
  34. 34.What is the average of 14, 21, 16, 16, 37 and 46? (a) 30 (b) 25 (c) 24 (d) 26
  35. 35.What is the average of all the whole numbers from 42 to 80? (a) 61 (b) 38 (c) 19 (d) 62
  36. 36.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) 44 (b) 39 (c) 54 (d) 20
  37. 37.The average of 5 numbers is 50. When one number is taken away, the average of the rest is 49. Which number was taken away? (a) 5 (b) 50 (c) 99 (d) 54
  38. 38.A batter has an average of 21 runs in 8 matches. How many runs are needed in the next match to raise the average to 24? (a) 24 (b) 48 (c) 27 (d) 49
  39. 39.A batter has an average of 30 runs in 8 matches. How many runs are needed in the next match to raise the average to 32? (a) 34 (b) 48 (c) 32 (d) 18
  40. 40.The average of 4 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) 44 (d) 16

Answer key

  1. 39
  2. 25
  3. 47
  4. 55
  5. 57
  6. 109
  7. 20
  8. 72
  9. 26
  10. 45
  11. 66
  12. 23
  13. 99
  14. 103
  15. 20
  16. 31
  17. 26
  18. 44
  19. 2
  20. 42
  21. 40
  22. 21
  23. 67
  24. 55
  25. 29
  26. 54
  27. 65
  28. 62
  29. 31
  30. 23
  31. 63
  32. 23
  33. 56
  34. 25
  35. 61
  36. 54
  37. 54
  38. 48
  39. 48
  40. 44

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