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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 994 · 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 27. When one number is taken away, the average of the rest is 26. Which number was taken away? (a) 27 (b) 53 (c) 32 (d) 6
  2. 2.The average of 6 numbers is 22. When one number is taken away, the average of the rest is 25. Which number was taken away? (a) 47 (b) 8 (c) 22 (d) 7
  3. 3.What is the average of all the whole numbers from 24 to 48? (a) 37 (b) 24 (c) 36 (d) 12
  4. 4.What is the average of 41, 48, 42 and 9? (a) 34 (b) 36 (c) 35 (d) 37
  5. 5.The average of 4 numbers is 49. When one number is taken away, the average of the rest is 44. Which number was taken away? (a) 49 (b) 64 (c) 93 (d) 20
  6. 6.What is the average of all the whole numbers from 16 to 34? (a) 25 (b) 26 (c) 18 (d) 9
  7. 7.The average of 7 numbers is 19. When one number is taken away, the average of the rest is 18. Which number was taken away? (a) 19 (b) 37 (c) 7 (d) 25
  8. 8.A batter has an average of 54 runs in 4 matches. How many runs are needed in the next match to raise the average to 61? (a) 35 (b) 89 (c) 68 (d) 61
  9. 9.The average of 5 numbers is 50. When one number is taken away, the average of the rest is 49. Which number was taken away? (a) 54 (b) 99 (c) 5 (d) 50
  10. 10.A batter has an average of 27 runs in 8 matches. How many runs are needed in the next match to raise the average to 35? (a) 35 (b) 72 (c) 99 (d) 43
  11. 11.What is the average of all the whole numbers from 29 to 45? (a) 8 (b) 38 (c) 16 (d) 37
  12. 12.A batter has an average of 49 runs in 7 matches. How many runs are needed in the next match to raise the average to 57? (a) 57 (b) 65 (c) 64 (d) 113
  13. 13.The average of 8 numbers is 30. When one number is taken away, the average of the rest is 29. Which number was taken away? (a) 59 (b) 8 (c) 30 (d) 37
  14. 14.The average of 6 numbers is 30. When one number is taken away, the average of the rest is 29. Which number was taken away? (a) 30 (b) 35 (c) 6 (d) 59
  15. 15.What is the average of all the whole numbers from 55 to 91? (a) 18 (b) 36 (c) 74 (d) 73
  16. 16.What is the average of 45, 44, 30 and 29? (a) 39 (b) 38 (c) 37 (d) 36
  17. 17.What is the average of all the whole numbers from 39 to 65? (a) 53 (b) 26 (c) 52 (d) 13
  18. 18.What is the average of 63, 56, 80 and 73? (a) 67 (b) 69 (c) 70 (d) 68
  19. 19.The average of 7 numbers is 23. When one number is taken away, the average of the rest is 24. Which number was taken away? (a) 47 (b) 17 (c) 23 (d) 18
  20. 20.The average of 4 numbers is 41. When one number is taken away, the average of the rest is 40. Which number was taken away? (a) 4 (b) 81 (c) 44 (d) 41
  21. 21.What is the average of 55, 41, 42, 65 and 67? (a) 55 (b) 56 (c) 53 (d) 54
  22. 22.What is the average of all the whole numbers from 11 to 29? (a) 20 (b) 21 (c) 9 (d) 18
  23. 23.The average of 4 numbers is 50. When one number is taken away, the average of the rest is 46. Which number was taken away? (a) 62 (b) 50 (c) 16 (d) 96
  24. 24.What is the average of 30, 17, 18, 30, 40 and 45? (a) 29 (b) 31 (c) 36 (d) 30
  25. 25.What is the average of all the whole numbers from 60 to 100? (a) 20 (b) 40 (c) 81 (d) 80
  26. 26.A batter has an average of 43 runs in 5 matches. How many runs are needed in the next match to raise the average to 45? (a) 45 (b) 47 (c) 55 (d) 12
  27. 27.What is the average of all the whole numbers from 13 to 35? (a) 25 (b) 11 (c) 22 (d) 24
  28. 28.What is the average of 65, 61, 65, 67 and 17? (a) 55 (b) 57 (c) 54 (d) 56
  29. 29.A batter has an average of 54 runs in 7 matches. How many runs are needed in the next match to raise the average to 59? (a) 40 (b) 94 (c) 59 (d) 64
  30. 30.A batter has an average of 22 runs in 7 matches. How many runs are needed in the next match to raise the average to 26? (a) 54 (b) 26 (c) 30 (d) 32
  31. 31.What is the average of all the whole numbers from 11 to 27? (a) 8 (b) 16 (c) 20 (d) 19
  32. 32.A batter has an average of 54 runs in 3 matches. How many runs are needed in the next match to raise the average to 62? (a) 70 (b) 62 (c) 32 (d) 86
  33. 33.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) 64 (b) 79 (c) 21 (d) 61
  34. 34.The average of 5 numbers is 24. When one number is taken away, the average of the rest is 23. Which number was taken away? (a) 5 (b) 28 (c) 24 (d) 47
  35. 35.A batter has an average of 36 runs in 7 matches. How many runs are needed in the next match to raise the average to 42? (a) 42 (b) 84 (c) 85 (d) 48
  36. 36.What is the average of 14, 16, 16, 36, 27 and 23? (a) 23 (b) 24 (c) 22 (d) 21
  37. 37.What is the average of 52, 73, 69 and 58? (a) 62 (b) 84 (c) 64 (d) 63
  38. 38.What is the average of 55, 38, 55, 33, 31 and 40? (a) 44 (b) 42 (c) 43 (d) 41
  39. 39.The average of 7 numbers is 16. When one number is taken away, the average of the rest is 18. Which number was taken away? (a) 5 (b) 16 (c) 34 (d) 4
  40. 40.The average of 5 numbers is 11. When one number is taken away, the average of the rest is 10. Which number was taken away? (a) 5 (b) 15 (c) 11 (d) 21

Answer key

  1. 32
  2. 7
  3. 36
  4. 35
  5. 64
  6. 25
  7. 25
  8. 89
  9. 54
  10. 99
  11. 37
  12. 113
  13. 37
  14. 35
  15. 73
  16. 37
  17. 52
  18. 68
  19. 17
  20. 44
  21. 54
  22. 20
  23. 62
  24. 30
  25. 80
  26. 55
  27. 24
  28. 55
  29. 94
  30. 54
  31. 19
  32. 86
  33. 79
  34. 28
  35. 84
  36. 22
  37. 63
  38. 42
  39. 4
  40. 15

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