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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 598 · 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 19. Which number was taken away? (a) 17 (b) 36 (c) 10 (d) 9
  2. 2.The average of 8 numbers is 38. When one number is taken away, the average of the rest is 43. Which number was taken away? (a) 38 (b) 4 (c) 81 (d) 3
  3. 3.A batter has an average of 36 runs in 4 matches. How many runs are needed in the next match to raise the average to 38? (a) 10 (b) 40 (c) 46 (d) 38
  4. 4.A batter has an average of 24 runs in 9 matches. How many runs are needed in the next match to raise the average to 30? (a) 36 (b) 84 (c) 30 (d) 60
  5. 5.What is the average of all the whole numbers from 48 to 88? (a) 20 (b) 40 (c) 69 (d) 68
  6. 6.What is the average of all the whole numbers from 59 to 79? (a) 70 (b) 10 (c) 20 (d) 69
  7. 7.The average of 6 numbers is 35. When one number is taken away, the average of the rest is 32. Which number was taken away? (a) 35 (b) 67 (c) 18 (d) 50
  8. 8.A batter has an average of 33 runs in 9 matches. How many runs are needed in the next match to raise the average to 35? (a) 37 (b) 53 (c) 20 (d) 35
  9. 9.A batter has an average of 33 runs in 8 matches. How many runs are needed in the next match to raise the average to 41? (a) 41 (b) 72 (c) 105 (d) 49
  10. 10.The average of 6 numbers is 45. When one number is taken away, the average of the rest is 44. Which number was taken away? (a) 50 (b) 89 (c) 45 (d) 6
  11. 11.The average of 4 numbers is 39. When one number is taken away, the average of the rest is 36. Which number was taken away? (a) 75 (b) 48 (c) 39 (d) 12
  12. 12.What is the average of all the whole numbers from 45 to 75? (a) 15 (b) 61 (c) 30 (d) 60
  13. 13.The average of 6 numbers is 13. When one number is taken away, the average of the rest is 11. Which number was taken away? (a) 13 (b) 24 (c) 12 (d) 23
  14. 14.What is the average of all the whole numbers from 41 to 65? (a) 24 (b) 12 (c) 53 (d) 54
  15. 15.What is the average of all the whole numbers from 56 to 88? (a) 72 (b) 73 (c) 16 (d) 32
  16. 16.What is the average of 55, 64, 63, 80, 53 and 75? (a) 66 (b) 64 (c) 65 (d) 78
  17. 17.A batter has an average of 55 runs in 3 matches. How many runs are needed in the next match to raise the average to 58? (a) 12 (b) 67 (c) 61 (d) 58
  18. 18.What is the average of all the whole numbers from 53 to 91? (a) 38 (b) 19 (c) 72 (d) 73
  19. 19.The average of 8 numbers is 25. When one number is taken away, the average of the rest is 21. Which number was taken away? (a) 25 (b) 32 (c) 53 (d) 46
  20. 20.What is the average of all the whole numbers from 52 to 72? (a) 63 (b) 62 (c) 10 (d) 20
  21. 21.What is the average of all the whole numbers from 32 to 72? (a) 40 (b) 20 (c) 53 (d) 52
  22. 22.The average of 6 numbers is 17. When one number is taken away, the average of the rest is 16. Which number was taken away? (a) 17 (b) 33 (c) 6 (d) 22
  23. 23.The average of 8 numbers is 33. When one number is taken away, the average of the rest is 32. Which number was taken away? (a) 65 (b) 40 (c) 8 (d) 33
  24. 24.What is the average of all the whole numbers from 26 to 60? (a) 34 (b) 17 (c) 43 (d) 44
  25. 25.What is the average of all the whole numbers from 10 to 16? (a) 13 (b) 6 (c) 3 (d) 14
  26. 26.What is the average of all the whole numbers from 48 to 86? (a) 19 (b) 38 (c) 68 (d) 67
  27. 27.The average of 6 numbers is 26. When one number is taken away, the average of the rest is 21. Which number was taken away? (a) 51 (b) 47 (c) 26 (d) 30
  28. 28.What is the average of all the whole numbers from 47 to 85? (a) 38 (b) 67 (c) 66 (d) 19
  29. 29.A batter has an average of 27 runs in 9 matches. How many runs are needed in the next match to raise the average to 30? (a) 30 (b) 33 (c) 58 (d) 57
  30. 30.What is the average of 12, 19, 36, 39, 24 and 32? (a) 28 (b) 26 (c) 27 (d) 29
  31. 31.What is the average of all the whole numbers from 53 to 63? (a) 59 (b) 5 (c) 10 (d) 58
  32. 32.What is the average of all the whole numbers from 54 to 74? (a) 64 (b) 65 (c) 20 (d) 10
  33. 33.What is the average of all the whole numbers from 52 to 78? (a) 65 (b) 13 (c) 26 (d) 66
  34. 34.What is the average of all the whole numbers from 6 to 30? (a) 24 (b) 12 (c) 19 (d) 18
  35. 35.What is the average of 18, 32, 13 and 49? (a) 27 (b) 29 (c) 30 (d) 28
  36. 36.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 49? (a) 49 (b) 55 (c) 8 (d) 51
  37. 37.The average of 4 numbers is 11. When one number is taken away, the average of the rest is 6. Which number was taken away? (a) 11 (b) 20 (c) 17 (d) 26
  38. 38.A batter has an average of 58 runs in 6 matches. How many runs are needed in the next match to raise the average to 61? (a) 79 (b) 21 (c) 64 (d) 61
  39. 39.A batter has an average of 20 runs in 8 matches. How many runs are needed in the next match to raise the average to 28? (a) 92 (b) 28 (c) 72 (d) 36
  40. 40.The average of 7 numbers is 38. When one number is taken away, the average of the rest is 35. Which number was taken away? (a) 38 (b) 21 (c) 73 (d) 56

Answer key

  1. 9
  2. 3
  3. 46
  4. 84
  5. 68
  6. 69
  7. 50
  8. 53
  9. 105
  10. 50
  11. 48
  12. 60
  13. 23
  14. 53
  15. 72
  16. 65
  17. 67
  18. 72
  19. 53
  20. 62
  21. 52
  22. 22
  23. 40
  24. 43
  25. 13
  26. 67
  27. 51
  28. 66
  29. 57
  30. 27
  31. 58
  32. 64
  33. 65
  34. 18
  35. 28
  36. 55
  37. 26
  38. 79
  39. 92
  40. 56

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