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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 98 · 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 7 numbers is 44. When one number is taken away, the average of the rest is 42. Which number was taken away? (a) 44 (b) 14 (c) 56 (d) 86
  2. 2.A batter has an average of 28 runs in 4 matches. How many runs are needed in the next match to raise the average to 32? (a) 32 (b) 48 (c) 36 (d) 20
  3. 3.What is the average of all the whole numbers from 7 to 19? (a) 14 (b) 12 (c) 13 (d) 6
  4. 4.The average of 8 numbers is 39. When one number is taken away, the average of the rest is 38. Which number was taken away? (a) 8 (b) 39 (c) 46 (d) 77
  5. 5.The average of 5 numbers is 33. When one number is taken away, the average of the rest is 29. Which number was taken away? (a) 62 (b) 33 (c) 49 (d) 20
  6. 6.What is the average of 65, 72, 63, 71 and 14? (a) 59 (b) 58 (c) 57 (d) 56
  7. 7.The average of 8 numbers is 45. When one number is taken away, the average of the rest is 50. Which number was taken away? (a) 95 (b) 11 (c) 10 (d) 45
  8. 8.What is the average of 47, 66, 60, 47 and 60? (a) 57 (b) 70 (c) 55 (d) 56
  9. 9.What is the average of 65, 58, 41 and 36? (a) 49 (b) 52 (c) 51 (d) 50
  10. 10.The average of 4 numbers is 16. When one number is taken away, the average of the rest is 13. Which number was taken away? (a) 12 (b) 29 (c) 16 (d) 25
  11. 11.The average of 4 numbers is 21. When one number is taken away, the average of the rest is 23. Which number was taken away? (a) 21 (b) 44 (c) 16 (d) 15
  12. 12.What is the average of all the whole numbers from 17 to 43? (a) 31 (b) 30 (c) 26 (d) 13
  13. 13.What is the average of all the whole numbers from 30 to 42? (a) 6 (b) 12 (c) 37 (d) 36
  14. 14.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 48? (a) 51 (b) 30 (c) 75 (d) 48
  15. 15.The average of 6 numbers is 37. When one number is taken away, the average of the rest is 38. Which number was taken away? (a) 33 (b) 32 (c) 37 (d) 75
  16. 16.A batter has an average of 24 runs in 8 matches. How many runs are needed in the next match to raise the average to 27? (a) 27 (b) 30 (c) 51 (d) 52
  17. 17.What is the average of 19, 28, 19, 28, 25 and 67? (a) 30 (b) 33 (c) 32 (d) 31
  18. 18.What is the average of 78, 75, 51, 54, 63 and 75? (a) 65 (b) 67 (c) 68 (d) 66
  19. 19.A batter has an average of 35 runs in 5 matches. How many runs are needed in the next match to raise the average to 40? (a) 30 (b) 45 (c) 40 (d) 65
  20. 20.A batter has an average of 20 runs in 9 matches. How many runs are needed in the next match to raise the average to 28? (a) 80 (b) 28 (c) 100 (d) 36
  21. 21.A batter has an average of 42 runs in 4 matches. How many runs are needed in the next match to raise the average to 49? (a) 35 (b) 77 (c) 56 (d) 49
  22. 22.A batter has an average of 37 runs in 3 matches. How many runs are needed in the next match to raise the average to 42? (a) 47 (b) 42 (c) 57 (d) 20
  23. 23.The average of 4 numbers is 35. When one number is taken away, the average of the rest is 40. Which number was taken away? (a) 21 (b) 75 (c) 20 (d) 35
  24. 24.What is the average of 76, 66, 54, 74, 65 and 73? (a) 68 (b) 70 (c) 69 (d) 67
  25. 25.What is the average of all the whole numbers from 51 to 87? (a) 18 (b) 36 (c) 69 (d) 70
  26. 26.The average of 4 numbers is 39. When one number is taken away, the average of the rest is 40. Which number was taken away? (a) 79 (b) 37 (c) 36 (d) 39
  27. 27.The average of 5 numbers is 41. When one number is taken away, the average of the rest is 42. Which number was taken away? (a) 83 (b) 38 (c) 37 (d) 41
  28. 28.What is the average of all the whole numbers from 25 to 63? (a) 38 (b) 44 (c) 45 (d) 19
  29. 29.What is the average of 42, 37, 45 and 80? (a) 50 (b) 51 (c) 68 (d) 52
  30. 30.What is the average of 40, 19, 24 and 37? (a) 40 (b) 30 (c) 29 (d) 31
  31. 31.A batter has an average of 57 runs in 5 matches. How many runs are needed in the next match to raise the average to 60? (a) 60 (b) 75 (c) 63 (d) 18
  32. 32.What is the average of 53, 62, 57, 65 and 83? (a) 80 (b) 64 (c) 65 (d) 63
  33. 33.What is the average of 26, 35, 36 and 11? (a) 27 (b) 26 (c) 28 (d) 36
  34. 34.A batter has an average of 60 runs in 3 matches. How many runs are needed in the next match to raise the average to 68? (a) 76 (b) 92 (c) 32 (d) 68
  35. 35.What is the average of all the whole numbers from 32 to 52? (a) 43 (b) 20 (c) 10 (d) 42
  36. 36.What is the average of all the whole numbers from 39 to 77? (a) 38 (b) 58 (c) 19 (d) 59
  37. 37.What is the average of all the whole numbers from 13 to 47? (a) 34 (b) 17 (c) 31 (d) 30
  38. 38.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 37? (a) 58 (b) 44 (c) 28 (d) 37
  39. 39.A batter has an average of 44 runs in 4 matches. How many runs are needed in the next match to raise the average to 46? (a) 48 (b) 10 (c) 54 (d) 46
  40. 40.The average of 7 numbers is 11. When one number is taken away, the average of the rest is 8. Which number was taken away? (a) 11 (b) 29 (c) 19 (d) 21

Answer key

  1. 56
  2. 48
  3. 13
  4. 46
  5. 49
  6. 57
  7. 10
  8. 56
  9. 50
  10. 25
  11. 15
  12. 30
  13. 36
  14. 75
  15. 32
  16. 51
  17. 31
  18. 66
  19. 65
  20. 100
  21. 77
  22. 57
  23. 20
  24. 68
  25. 69
  26. 36
  27. 37
  28. 44
  29. 51
  30. 30
  31. 75
  32. 64
  33. 27
  34. 92
  35. 42
  36. 58
  37. 30
  38. 58
  39. 54
  40. 29

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