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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 324 · 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 12. When one number is taken away, the average of the rest is 10. Which number was taken away? (a) 22 (b) 16 (c) 26 (d) 12
  2. 2.What is the average of all the whole numbers from 14 to 48? (a) 17 (b) 32 (c) 34 (d) 31
  3. 3.What is the average of 59, 59, 44, 55 and 58? (a) 57 (b) 54 (c) 56 (d) 55
  4. 4.What is the average of all the whole numbers from 16 to 44? (a) 28 (b) 30 (c) 31 (d) 14
  5. 5.The average of 6 numbers is 29. When one number is taken away, the average of the rest is 33. Which number was taken away? (a) 10 (b) 62 (c) 9 (d) 29
  6. 6.What is the average of 23, 42, 16 and 27? (a) 36 (b) 27 (c) 28 (d) 26
  7. 7.What is the average of all the whole numbers from 9 to 15? (a) 6 (b) 12 (c) 3 (d) 13
  8. 8.What is the average of all the whole numbers from 20 to 34? (a) 7 (b) 28 (c) 27 (d) 14
  9. 9.What is the average of 73, 77, 68, 66 and 56? (a) 69 (b) 85 (c) 67 (d) 68
  10. 10.The average of 4 numbers is 19. When one number is taken away, the average of the rest is 18. Which number was taken away? (a) 22 (b) 37 (c) 19 (d) 4
  11. 11.The average of 8 numbers is 39. When one number is taken away, the average of the rest is 34. Which number was taken away? (a) 74 (b) 39 (c) 40 (d) 73
  12. 12.What is the average of 59, 64, 82, 69 and 76? (a) 71 (b) 69 (c) 70 (d) 72
  13. 13.The average of 7 numbers is 20. When one number is taken away, the average of the rest is 17. Which number was taken away? (a) 21 (b) 20 (c) 38 (d) 37
  14. 14.A batter has an average of 39 runs in 8 matches. How many runs are needed in the next match to raise the average to 45? (a) 54 (b) 45 (c) 93 (d) 51
  15. 15.What is the average of 46, 43, 44, 39 and 58? (a) 47 (b) 48 (c) 46 (d) 45
  16. 16.The average of 8 numbers is 20. When one number is taken away, the average of the rest is 18. Which number was taken away? (a) 34 (b) 20 (c) 16 (d) 38
  17. 17.What is the average of all the whole numbers from 5 to 19? (a) 14 (b) 12 (c) 13 (d) 7
  18. 18.What is the average of 19, 37, 21 and 51? (a) 31 (b) 33 (c) 32 (d) 34
  19. 19.What is the average of 41, 29, 26, 38, 48 and 34? (a) 36 (b) 37 (c) 35 (d) 38
  20. 20.The average of 4 numbers is 43. When one number is taken away, the average of the rest is 40. Which number was taken away? (a) 52 (b) 12 (c) 43 (d) 83
  21. 21.A batter has an average of 40 runs in 3 matches. How many runs are needed in the next match to raise the average to 42? (a) 48 (b) 44 (c) 8 (d) 42
  22. 22.The average of 4 numbers is 29. When one number is taken away, the average of the rest is 31. Which number was taken away? (a) 23 (b) 29 (c) 60 (d) 24
  23. 23.A batter has an average of 53 runs in 6 matches. How many runs are needed in the next match to raise the average to 60? (a) 49 (b) 102 (c) 67 (d) 60
  24. 24.The average of 8 numbers is 45. When one number is taken away, the average of the rest is 44. Which number was taken away? (a) 52 (b) 8 (c) 89 (d) 45
  25. 25.A batter has an average of 53 runs in 4 matches. How many runs are needed in the next match to raise the average to 61? (a) 93 (b) 40 (c) 69 (d) 61
  26. 26.What is the average of 28, 50, 50, 57 and 25? (a) 44 (b) 41 (c) 43 (d) 42
  27. 27.What is the average of 39, 50, 63, 65, 50 and 51? (a) 52 (b) 55 (c) 53 (d) 54
  28. 28.A batter has an average of 28 runs in 7 matches. How many runs are needed in the next match to raise the average to 30? (a) 32 (b) 16 (c) 44 (d) 30
  29. 29.What is the average of 65, 62, 64, 57 and 17? (a) 54 (b) 55 (c) 52 (d) 53
  30. 30.A batter has an average of 32 runs in 7 matches. How many runs are needed in the next match to raise the average to 38? (a) 44 (b) 48 (c) 80 (d) 38
  31. 31.The average of 6 numbers is 48. When one number is taken away, the average of the rest is 53. Which number was taken away? (a) 48 (b) 101 (c) 24 (d) 23
  32. 32.What is the average of 55, 71, 66 and 84? (a) 70 (b) 92 (c) 68 (d) 69
  33. 33.What is the average of 66, 60, 66 and 88? (a) 69 (b) 70 (c) 72 (d) 71
  34. 34.What is the average of 17, 28, 41, 13, 21 and 36? (a) 25 (b) 27 (c) 28 (d) 26
  35. 35.What is the average of all the whole numbers from 50 to 74? (a) 63 (b) 24 (c) 12 (d) 62
  36. 36.The average of 4 numbers is 32. When one number is taken away, the average of the rest is 36. Which number was taken away? (a) 68 (b) 21 (c) 20 (d) 32
  37. 37.What is the average of all the whole numbers from 59 to 95? (a) 77 (b) 18 (c) 36 (d) 78
  38. 38.The average of 7 numbers is 20. When one number is taken away, the average of the rest is 21. Which number was taken away? (a) 41 (b) 14 (c) 20 (d) 15
  39. 39.The average of 4 numbers is 38. When one number is taken away, the average of the rest is 35. Which number was taken away? (a) 12 (b) 47 (c) 38 (d) 73
  40. 40.The average of 4 numbers is 11. When one number is taken away, the average of the rest is 13. Which number was taken away? (a) 5 (b) 11 (c) 24 (d) 6

Answer key

  1. 26
  2. 31
  3. 55
  4. 30
  5. 9
  6. 27
  7. 12
  8. 27
  9. 68
  10. 22
  11. 74
  12. 70
  13. 38
  14. 93
  15. 46
  16. 34
  17. 12
  18. 32
  19. 36
  20. 52
  21. 48
  22. 23
  23. 102
  24. 52
  25. 93
  26. 42
  27. 53
  28. 44
  29. 53
  30. 80
  31. 23
  32. 69
  33. 70
  34. 26
  35. 62
  36. 20
  37. 77
  38. 14
  39. 47
  40. 5

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