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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 206 · 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 4 numbers is 48. When one number is taken away, the average of the rest is 43. Which number was taken away? (a) 48 (b) 20 (c) 91 (d) 63
  2. 2.The average of 5 numbers is 32. When one number is taken away, the average of the rest is 35. Which number was taken away? (a) 67 (b) 32 (c) 20 (d) 21
  3. 3.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 40? (a) 47 (b) 70 (c) 103 (d) 40
  4. 4.What is the average of all the whole numbers from 41 to 71? (a) 15 (b) 56 (c) 30 (d) 57
  5. 5.A batter has an average of 37 runs in 8 matches. How many runs are needed in the next match to raise the average to 45? (a) 45 (b) 72 (c) 109 (d) 53
  6. 6.What is the average of 57, 39, 46 and 66? (a) 51 (b) 54 (c) 53 (d) 52
  7. 7.What is the average of 53, 57, 44, 43, 42 and 25? (a) 46 (b) 45 (c) 43 (d) 44
  8. 8.What is the average of 68, 79, 77, 68 and 58? (a) 70 (b) 69 (c) 72 (d) 71
  9. 9.The average of 4 numbers is 21. When one number is taken away, the average of the rest is 25. Which number was taken away? (a) 46 (b) 10 (c) 21 (d) 9
  10. 10.What is the average of 71, 82, 83 and 80? (a) 81 (b) 78 (c) 80 (d) 79
  11. 11.The average of 8 numbers is 16. When one number is taken away, the average of the rest is 13. Which number was taken away? (a) 37 (b) 29 (c) 16 (d) 24
  12. 12.What is the average of 22, 20, 22 and 76? (a) 34 (b) 35 (c) 37 (d) 36
  13. 13.The average of 7 numbers is 34. When one number is taken away, the average of the rest is 30. Which number was taken away? (a) 28 (b) 34 (c) 58 (d) 64
  14. 14.A batter has an average of 51 runs in 6 matches. How many runs are needed in the next match to raise the average to 58? (a) 58 (b) 49 (c) 65 (d) 100
  15. 15.The average of 4 numbers is 22. When one number is taken away, the average of the rest is 20. Which number was taken away? (a) 28 (b) 8 (c) 42 (d) 22
  16. 16.The average of 7 numbers is 19. When one number is taken away, the average of the rest is 21. Which number was taken away? (a) 19 (b) 8 (c) 7 (d) 40
  17. 17.The average of 4 numbers is 25. When one number is taken away, the average of the rest is 23. Which number was taken away? (a) 25 (b) 48 (c) 8 (d) 31
  18. 18.A batter has an average of 39 runs in 9 matches. How many runs are needed in the next match to raise the average to 44? (a) 89 (b) 44 (c) 50 (d) 49
  19. 19.What is the average of 65, 74, 84, 61 and 71? (a) 70 (b) 71 (c) 72 (d) 73
  20. 20.The average of 4 numbers is 20. When one number is taken away, the average of the rest is 21. Which number was taken away? (a) 18 (b) 41 (c) 20 (d) 17
  21. 21.What is the average of 93, 68, 69, 84, 71 and 89? (a) 81 (b) 79 (c) 78 (d) 80
  22. 22.What is the average of 14, 39, 11, 37 and 29? (a) 25 (b) 27 (c) 26 (d) 28
  23. 23.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 30? (a) 30 (b) 33 (c) 48 (d) 21
  24. 24.A batter has an average of 36 runs in 9 matches. How many runs are needed in the next match to raise the average to 43? (a) 106 (b) 43 (c) 50 (d) 70
  25. 25.The average of 5 numbers is 32. When one number is taken away, the average of the rest is 33. Which number was taken away? (a) 32 (b) 28 (c) 65 (d) 29
  26. 26.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 24? (a) 26 (b) 24 (c) 34 (d) 12
  27. 27.The average of 8 numbers is 20. When one number is taken away, the average of the rest is 19. Which number was taken away? (a) 27 (b) 8 (c) 39 (d) 20
  28. 28.What is the average of 28, 31, 50, 30 and 46? (a) 37 (b) 39 (c) 36 (d) 38
  29. 29.What is the average of 73, 54, 68 and 53? (a) 64 (b) 61 (c) 62 (d) 63
  30. 30.What is the average of all the whole numbers from 41 to 67? (a) 55 (b) 54 (c) 13 (d) 26
  31. 31.A batter has an average of 31 runs in 6 matches. How many runs are needed in the next match to raise the average to 35? (a) 59 (b) 28 (c) 39 (d) 35
  32. 32.What is the average of all the whole numbers from 6 to 18? (a) 11 (b) 6 (c) 12 (d) 13
  33. 33.The average of 6 numbers is 33. When one number is taken away, the average of the rest is 32. Which number was taken away? (a) 65 (b) 38 (c) 6 (d) 33
  34. 34.What is the average of 30, 53, 56, 37, 43 and 39? (a) 43 (b) 44 (c) 45 (d) 42
  35. 35.The average of 5 numbers is 27. When one number is taken away, the average of the rest is 28. Which number was taken away? (a) 55 (b) 24 (c) 27 (d) 23
  36. 36.The average of 6 numbers is 35. When one number is taken away, the average of the rest is 36. Which number was taken away? (a) 35 (b) 71 (c) 30 (d) 31
  37. 37.What is the average of all the whole numbers from 33 to 49? (a) 16 (b) 8 (c) 42 (d) 41
  38. 38.A batter has an average of 23 runs in 9 matches. How many runs are needed in the next match to raise the average to 26? (a) 26 (b) 30 (c) 29 (d) 53
  39. 39.What is the average of 69, 82, 82 and 75? (a) 79 (b) 78 (c) 77 (d) 76
  40. 40.What is the average of 52, 44, 33, 36 and 75? (a) 49 (b) 60 (c) 47 (d) 48

Answer key

  1. 63
  2. 20
  3. 103
  4. 56
  5. 109
  6. 52
  7. 44
  8. 70
  9. 9
  10. 79
  11. 37
  12. 35
  13. 58
  14. 100
  15. 28
  16. 7
  17. 31
  18. 89
  19. 71
  20. 17
  21. 79
  22. 26
  23. 48
  24. 106
  25. 28
  26. 34
  27. 27
  28. 37
  29. 62
  30. 54
  31. 59
  32. 12
  33. 38
  34. 43
  35. 23
  36. 30
  37. 41
  38. 53
  39. 77
  40. 48

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