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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 655 · 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 45. When one number is taken away, the average of the rest is 48. Which number was taken away? (a) 34 (b) 33 (c) 45 (d) 93
  2. 2.The average of 6 numbers is 22. When one number is taken away, the average of the rest is 20. Which number was taken away? (a) 22 (b) 32 (c) 12 (d) 42
  3. 3.A batter has an average of 33 runs in 3 matches. How many runs are needed in the next match to raise the average to 38? (a) 20 (b) 43 (c) 53 (d) 38
  4. 4.A batter has an average of 20 runs in 3 matches. How many runs are needed in the next match to raise the average to 24? (a) 28 (b) 24 (c) 16 (d) 36
  5. 5.A batter has an average of 45 runs in 9 matches. How many runs are needed in the next match to raise the average to 51? (a) 57 (b) 51 (c) 60 (d) 105
  6. 6.A batter has an average of 29 runs in 7 matches. How many runs are needed in the next match to raise the average to 31? (a) 16 (b) 31 (c) 33 (d) 45
  7. 7.The average of 4 numbers is 30. When one number is taken away, the average of the rest is 35. Which number was taken away? (a) 30 (b) 16 (c) 15 (d) 65
  8. 8.What is the average of all the whole numbers from 15 to 53? (a) 35 (b) 34 (c) 19 (d) 38
  9. 9.A batter has an average of 56 runs in 7 matches. How many runs are needed in the next match to raise the average to 60? (a) 64 (b) 32 (c) 60 (d) 88
  10. 10.What is the average of 70, 53, 44 and 57? (a) 58 (b) 55 (c) 56 (d) 57
  11. 11.The average of 6 numbers is 10. When one number is taken away, the average of the rest is 8. Which number was taken away? (a) 12 (b) 18 (c) 20 (d) 10
  12. 12.What is the average of 63, 69, 42 and 54? (a) 57 (b) 56 (c) 76 (d) 58
  13. 13.What is the average of all the whole numbers from 25 to 65? (a) 20 (b) 46 (c) 40 (d) 45
  14. 14.The average of 6 numbers is 40. When one number is taken away, the average of the rest is 37. Which number was taken away? (a) 77 (b) 55 (c) 18 (d) 40
  15. 15.The average of 4 numbers is 28. When one number is taken away, the average of the rest is 33. Which number was taken away? (a) 28 (b) 13 (c) 61 (d) 14
  16. 16.What is the average of all the whole numbers from 7 to 15? (a) 12 (b) 4 (c) 11 (d) 8
  17. 17.The average of 5 numbers is 20. When one number is taken away, the average of the rest is 15. Which number was taken away? (a) 25 (b) 40 (c) 20 (d) 35
  18. 18.What is the average of all the whole numbers from 7 to 17? (a) 12 (b) 10 (c) 5 (d) 13
  19. 19.What is the average of 54, 47, 56 and 55? (a) 53 (b) 54 (c) 52 (d) 55
  20. 20.A batter has an average of 27 runs in 6 matches. How many runs are needed in the next match to raise the average to 34? (a) 76 (b) 41 (c) 34 (d) 49
  21. 21.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) 12 (b) 54 (c) 63 (d) 57
  22. 22.What is the average of 56, 53, 61 and 94? (a) 88 (b) 65 (c) 66 (d) 67
  23. 23.What is the average of all the whole numbers from 33 to 41? (a) 38 (b) 4 (c) 8 (d) 37
  24. 24.What is the average of 32, 43, 51 and 58? (a) 48 (b) 46 (c) 45 (d) 47
  25. 25.The average of 6 numbers is 43. When one number is taken away, the average of the rest is 45. Which number was taken away? (a) 43 (b) 34 (c) 33 (d) 88
  26. 26.What is the average of 14, 20, 27, 26, 26 and 25? (a) 23 (b) 22 (c) 25 (d) 24
  27. 27.The average of 8 numbers is 28. When one number is taken away, the average of the rest is 24. Which number was taken away? (a) 32 (b) 28 (c) 52 (d) 56
  28. 28.A batter has an average of 20 runs in 4 matches. How many runs are needed in the next match to raise the average to 28? (a) 28 (b) 40 (c) 36 (d) 60
  29. 29.What is the average of 51, 36, 62, 36, 57 and 52? (a) 48 (b) 49 (c) 51 (d) 50
  30. 30.The average of 4 numbers is 41. When one number is taken away, the average of the rest is 40. Which number was taken away? (a) 81 (b) 44 (c) 4 (d) 41
  31. 31.The average of 4 numbers is 37. When one number is taken away, the average of the rest is 36. Which number was taken away? (a) 73 (b) 4 (c) 37 (d) 40
  32. 32.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) 50 (b) 101 (c) 61 (d) 56
  33. 33.What is the average of all the whole numbers from 11 to 37? (a) 24 (b) 25 (c) 26 (d) 13
  34. 34.What is the average of 18, 10, 35 and 21? (a) 28 (b) 20 (c) 21 (d) 22
  35. 35.The average of 7 numbers is 40. When one number is taken away, the average of the rest is 37. Which number was taken away? (a) 21 (b) 58 (c) 40 (d) 77
  36. 36.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 38? (a) 62 (b) 38 (c) 32 (d) 46
  37. 37.The average of 8 numbers is 23. When one number is taken away, the average of the rest is 24. Which number was taken away? (a) 16 (b) 47 (c) 23 (d) 17
  38. 38.A batter has an average of 22 runs in 3 matches. How many runs are needed in the next match to raise the average to 25? (a) 34 (b) 25 (c) 28 (d) 12
  39. 39.A batter has an average of 41 runs in 9 matches. How many runs are needed in the next match to raise the average to 44? (a) 44 (b) 71 (c) 47 (d) 30
  40. 40.A batter has an average of 37 runs in 7 matches. How many runs are needed in the next match to raise the average to 45? (a) 101 (b) 64 (c) 53 (d) 45

Answer key

  1. 33
  2. 32
  3. 53
  4. 36
  5. 105
  6. 45
  7. 15
  8. 34
  9. 88
  10. 56
  11. 20
  12. 57
  13. 45
  14. 55
  15. 13
  16. 11
  17. 40
  18. 12
  19. 53
  20. 76
  21. 63
  22. 66
  23. 37
  24. 46
  25. 33
  26. 23
  27. 56
  28. 60
  29. 49
  30. 44
  31. 40
  32. 101
  33. 24
  34. 21
  35. 58
  36. 62
  37. 16
  38. 34
  39. 71
  40. 101

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