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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 161 · 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 6 numbers is 25. When one number is taken away, the average of the rest is 24. Which number was taken away? (a) 49 (b) 25 (c) 30 (d) 6
  2. 2.What is the average of 43, 44, 44 and 33? (a) 40 (b) 41 (c) 42 (d) 43
  3. 3.What is the average of 9, 11, 27, 13, 13 and 71? (a) 23 (b) 25 (c) 26 (d) 24
  4. 4.A batter has an average of 48 runs in 4 matches. How many runs are needed in the next match to raise the average to 56? (a) 40 (b) 88 (c) 64 (d) 56
  5. 5.What is the average of all the whole numbers from 43 to 51? (a) 47 (b) 4 (c) 48 (d) 8
  6. 6.A batter has an average of 28 runs in 6 matches. How many runs are needed in the next match to raise the average to 31? (a) 34 (b) 21 (c) 31 (d) 49
  7. 7.What is the average of 85, 63, 80 and 68? (a) 75 (b) 76 (c) 74 (d) 73
  8. 8.The average of 6 numbers is 12. When one number is taken away, the average of the rest is 7. Which number was taken away? (a) 19 (b) 30 (c) 12 (d) 37
  9. 9.What is the average of 26, 21, 28, 19 and 76? (a) 36 (b) 35 (c) 34 (d) 33
  10. 10.What is the average of 51, 35, 56, 44 and 49? (a) 46 (b) 49 (c) 48 (d) 47
  11. 11.The average of 8 numbers is 27. When one number is taken away, the average of the rest is 22. Which number was taken away? (a) 49 (b) 62 (c) 27 (d) 40
  12. 12.What is the average of all the whole numbers from 37 to 57? (a) 20 (b) 47 (c) 10 (d) 48
  13. 13.What is the average of all the whole numbers from 12 to 38? (a) 26 (b) 24 (c) 25 (d) 13
  14. 14.What is the average of 30, 48, 30, 47 and 15? (a) 35 (b) 33 (c) 34 (d) 36
  15. 15.What is the average of all the whole numbers from 25 to 55? (a) 30 (b) 40 (c) 15 (d) 41
  16. 16.What is the average of 73, 86, 79 and 50? (a) 71 (b) 96 (c) 73 (d) 72
  17. 17.The average of 8 numbers is 10. When one number is taken away, the average of the rest is 8. Which number was taken away? (a) 16 (b) 24 (c) 18 (d) 10
  18. 18.A batter has an average of 55 runs in 7 matches. How many runs are needed in the next match to raise the average to 58? (a) 24 (b) 79 (c) 58 (d) 61
  19. 19.What is the average of 65, 46, 55, 66 and 43? (a) 57 (b) 54 (c) 56 (d) 55
  20. 20.What is the average of 78, 57, 77, 82 and 51? (a) 71 (b) 68 (c) 69 (d) 70
  21. 21.A batter has an average of 24 runs in 4 matches. How many runs are needed in the next match to raise the average to 32? (a) 65 (b) 32 (c) 40 (d) 64
  22. 22.What is the average of 22, 31, 31 and 32? (a) 31 (b) 29 (c) 28 (d) 30
  23. 23.What is the average of 46, 38, 46, 59, 54 and 51? (a) 48 (b) 51 (c) 49 (d) 50
  24. 24.A batter has an average of 26 runs in 9 matches. How many runs are needed in the next match to raise the average to 34? (a) 106 (b) 34 (c) 80 (d) 42
  25. 25.The average of 6 numbers is 31. When one number is taken away, the average of the rest is 30. Which number was taken away? (a) 61 (b) 31 (c) 6 (d) 36
  26. 26.A batter has an average of 56 runs in 4 matches. How many runs are needed in the next match to raise the average to 63? (a) 70 (b) 63 (c) 91 (d) 35
  27. 27.A batter has an average of 52 runs in 4 matches. How many runs are needed in the next match to raise the average to 56? (a) 60 (b) 72 (c) 20 (d) 56
  28. 28.What is the average of 74, 78, 72 and 72? (a) 75 (b) 76 (c) 74 (d) 73
  29. 29.What is the average of 80, 72, 94, 77, 76 and 81? (a) 81 (b) 80 (c) 96 (d) 79
  30. 30.What is the average of all the whole numbers from 41 to 57? (a) 8 (b) 16 (c) 50 (d) 49
  31. 31.A batter has an average of 56 runs in 8 matches. How many runs are needed in the next match to raise the average to 59? (a) 62 (b) 59 (c) 27 (d) 83
  32. 32.The average of 6 numbers is 44. When one number is taken away, the average of the rest is 42. Which number was taken away? (a) 44 (b) 12 (c) 86 (d) 54
  33. 33.The average of 7 numbers is 48. When one number is taken away, the average of the rest is 50. Which number was taken away? (a) 37 (b) 48 (c) 98 (d) 36
  34. 34.What is the average of all the whole numbers from 7 to 31? (a) 12 (b) 24 (c) 19 (d) 20
  35. 35.The average of 5 numbers is 10. When one number is taken away, the average of the rest is 6. Which number was taken away? (a) 20 (b) 10 (c) 16 (d) 26
  36. 36.A batter has an average of 32 runs in 5 matches. How many runs are needed in the next match to raise the average to 34? (a) 36 (b) 44 (c) 34 (d) 12
  37. 37.What is the average of 10, 11, 13, 37, 34 and 33? (a) 22 (b) 24 (c) 23 (d) 25
  38. 38.What is the average of 73, 60, 66, 79 and 67? (a) 68 (b) 69 (c) 71 (d) 70
  39. 39.A batter has an average of 22 runs in 5 matches. How many runs are needed in the next match to raise the average to 27? (a) 27 (b) 32 (c) 30 (d) 52
  40. 40.The average of 4 numbers is 22. When one number is taken away, the average of the rest is 24. Which number was taken away? (a) 17 (b) 16 (c) 22 (d) 46

Answer key

  1. 30
  2. 41
  3. 24
  4. 88
  5. 47
  6. 49
  7. 74
  8. 37
  9. 34
  10. 47
  11. 62
  12. 47
  13. 25
  14. 34
  15. 40
  16. 72
  17. 24
  18. 79
  19. 55
  20. 69
  21. 64
  22. 29
  23. 49
  24. 106
  25. 36
  26. 91
  27. 72
  28. 74
  29. 80
  30. 49
  31. 83
  32. 54
  33. 36
  34. 19
  35. 26
  36. 44
  37. 23
  38. 69
  39. 52
  40. 16

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