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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 962 · 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 19. When one number is taken away, the average of the rest is 16. Which number was taken away? (a) 19 (b) 12 (c) 35 (d) 28
  2. 2.What is the average of 39, 21, 41, 36 and 8? (a) 29 (b) 28 (c) 31 (d) 30
  3. 3.What is the average of 42, 45, 52, 50 and 11? (a) 40 (b) 41 (c) 50 (d) 39
  4. 4.The average of 4 numbers is 40. When one number is taken away, the average of the rest is 42. Which number was taken away? (a) 82 (b) 34 (c) 35 (d) 40
  5. 5.The average of 6 numbers is 29. When one number is taken away, the average of the rest is 34. Which number was taken away? (a) 29 (b) 5 (c) 63 (d) 4
  6. 6.What is the average of 70, 93, 77 and 76? (a) 80 (b) 79 (c) 81 (d) 78
  7. 7.The average of 4 numbers is 21. When one number is taken away, the average of the rest is 19. Which number was taken away? (a) 27 (b) 8 (c) 21 (d) 40
  8. 8.A batter has an average of 41 runs in 3 matches. How many runs are needed in the next match to raise the average to 47? (a) 47 (b) 53 (c) 24 (d) 65
  9. 9.What is the average of all the whole numbers from 21 to 51? (a) 36 (b) 30 (c) 37 (d) 15
  10. 10.The average of 8 numbers is 21. When one number is taken away, the average of the rest is 17. Which number was taken away? (a) 32 (b) 38 (c) 21 (d) 49
  11. 11.The average of 5 numbers is 34. When one number is taken away, the average of the rest is 29. Which number was taken away? (a) 54 (b) 34 (c) 25 (d) 63
  12. 12.What is the average of all the whole numbers from 60 to 74? (a) 67 (b) 68 (c) 14 (d) 7
  13. 13.What is the average of 8, 11, 15, 18 and 58? (a) 22 (b) 23 (c) 21 (d) 24
  14. 14.The average of 7 numbers is 29. When one number is taken away, the average of the rest is 32. Which number was taken away? (a) 12 (b) 11 (c) 61 (d) 29
  15. 15.What is the average of all the whole numbers from 46 to 70? (a) 24 (b) 12 (c) 59 (d) 58
  16. 16.What is the average of 36, 49, 29, 41 and 20? (a) 37 (b) 35 (c) 36 (d) 34
  17. 17.What is the average of 26, 18, 28, 46, 44 and 30? (a) 33 (b) 31 (c) 34 (d) 32
  18. 18.What is the average of 43, 37, 42 and 14? (a) 35 (b) 36 (c) 34 (d) 33
  19. 19.What is the average of 31, 25, 54, 53 and 37? (a) 39 (b) 50 (c) 40 (d) 41
  20. 20.What is the average of 53, 52, 60, 59, 64 and 24? (a) 52 (b) 54 (c) 53 (d) 51
  21. 21.The average of 4 numbers is 13. When one number is taken away, the average of the rest is 12. Which number was taken away? (a) 25 (b) 16 (c) 13 (d) 4
  22. 22.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) 26 (b) 20 (c) 16 (d) 10
  23. 23.A batter has an average of 25 runs in 5 matches. How many runs are needed in the next match to raise the average to 31? (a) 37 (b) 36 (c) 61 (d) 31
  24. 24.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) 93 (c) 64 (d) 20
  25. 25.What is the average of 83, 82, 81, 86 and 28? (a) 90 (b) 72 (c) 73 (d) 71
  26. 26.What is the average of all the whole numbers from 5 to 39? (a) 23 (b) 34 (c) 17 (d) 22
  27. 27.What is the average of 62, 71, 67, 71, 75 and 38? (a) 65 (b) 64 (c) 66 (d) 63
  28. 28.A batter has an average of 42 runs in 7 matches. How many runs are needed in the next match to raise the average to 48? (a) 48 (b) 54 (c) 91 (d) 90
  29. 29.A batter has an average of 25 runs in 5 matches. How many runs are needed in the next match to raise the average to 30? (a) 30 (b) 56 (c) 55 (d) 35
  30. 30.What is the average of all the whole numbers from 6 to 12? (a) 9 (b) 3 (c) 10 (d) 6
  31. 31.The average of 7 numbers is 43. When one number is taken away, the average of the rest is 42. Which number was taken away? (a) 43 (b) 7 (c) 85 (d) 49
  32. 32.What is the average of 59, 65, 56, 51 and 29? (a) 65 (b) 52 (c) 53 (d) 51
  33. 33.A batter has an average of 24 runs in 9 matches. How many runs are needed in the next match to raise the average to 27? (a) 30 (b) 55 (c) 54 (d) 27
  34. 34.What is the average of 48, 51, 50 and 79? (a) 56 (b) 57 (c) 76 (d) 58
  35. 35.What is the average of all the whole numbers from 9 to 19? (a) 14 (b) 15 (c) 10 (d) 5
  36. 36.The average of 8 numbers is 32. When one number is taken away, the average of the rest is 34. Which number was taken away? (a) 66 (b) 19 (c) 32 (d) 18
  37. 37.A batter has an average of 26 runs in 6 matches. How many runs are needed in the next match to raise the average to 31? (a) 31 (b) 36 (c) 35 (d) 61
  38. 38.The average of 4 numbers is 22. When one number is taken away, the average of the rest is 19. Which number was taken away? (a) 31 (b) 41 (c) 22 (d) 12
  39. 39.What is the average of 34, 35, 24, 34 and 33? (a) 40 (b) 33 (c) 31 (d) 32
  40. 40.A batter has an average of 20 runs in 3 matches. How many runs are needed in the next match to raise the average to 24? (a) 24 (b) 28 (c) 36 (d) 16

Answer key

  1. 28
  2. 29
  3. 40
  4. 34
  5. 4
  6. 79
  7. 27
  8. 65
  9. 36
  10. 49
  11. 54
  12. 67
  13. 22
  14. 11
  15. 58
  16. 35
  17. 32
  18. 34
  19. 40
  20. 52
  21. 16
  22. 26
  23. 61
  24. 64
  25. 72
  26. 22
  27. 64
  28. 90
  29. 55
  30. 9
  31. 49
  32. 52
  33. 54
  34. 57
  35. 14
  36. 18
  37. 61
  38. 31
  39. 32
  40. 36

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