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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 468 · 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 33. When one number is taken away, the average of the rest is 36. Which number was taken away? (a) 33 (b) 69 (c) 16 (d) 15
  2. 2.The average of 6 numbers is 35. When one number is taken away, the average of the rest is 30. Which number was taken away? (a) 65 (b) 35 (c) 30 (d) 60
  3. 3.What is the average of 59, 61, 37 and 47? (a) 68 (b) 52 (c) 51 (d) 50
  4. 4.What is the average of 64, 52, 61 and 59? (a) 59 (b) 58 (c) 61 (d) 60
  5. 5.What is the average of 73, 81, 77, 88 and 56? (a) 75 (b) 77 (c) 74 (d) 76
  6. 6.What is the average of all the whole numbers from 58 to 72? (a) 7 (b) 14 (c) 65 (d) 66
  7. 7.What is the average of 38, 43, 48 and 31? (a) 42 (b) 39 (c) 40 (d) 41
  8. 8.What is the average of all the whole numbers from 7 to 37? (a) 30 (b) 15 (c) 23 (d) 22
  9. 9.What is the average of 20, 27, 18, 8 and 42? (a) 22 (b) 24 (c) 25 (d) 23
  10. 10.What is the average of 63, 68, 48, 51, 52 and 66? (a) 58 (b) 57 (c) 60 (d) 59
  11. 11.What is the average of 29, 15, 35, 24 and 32? (a) 29 (b) 28 (c) 26 (d) 27
  12. 12.What is the average of all the whole numbers from 38 to 62? (a) 12 (b) 51 (c) 24 (d) 50
  13. 13.A batter has an average of 22 runs in 9 matches. How many runs are needed in the next match to raise the average to 25? (a) 30 (b) 28 (c) 25 (d) 52
  14. 14.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) 31 (b) 35 (c) 30 (d) 71
  15. 15.The average of 8 numbers is 30. When one number is taken away, the average of the rest is 33. Which number was taken away? (a) 10 (b) 9 (c) 63 (d) 30
  16. 16.The average of 6 numbers is 24. When one number is taken away, the average of the rest is 22. Which number was taken away? (a) 12 (b) 34 (c) 46 (d) 24
  17. 17.A batter has an average of 35 runs in 4 matches. How many runs are needed in the next match to raise the average to 39? (a) 43 (b) 39 (c) 55 (d) 20
  18. 18.What is the average of 53, 56, 71, 71 and 89? (a) 69 (b) 85 (c) 68 (d) 67
  19. 19.The average of 5 numbers is 19. When one number is taken away, the average of the rest is 20. Which number was taken away? (a) 15 (b) 19 (c) 39 (d) 16
  20. 20.What is the average of all the whole numbers from 58 to 70? (a) 65 (b) 6 (c) 12 (d) 64
  21. 21.What is the average of 45, 23, 26, 33, 21 and 56? (a) 35 (b) 33 (c) 36 (d) 34
  22. 22.A batter has an average of 59 runs in 7 matches. How many runs are needed in the next match to raise the average to 65? (a) 48 (b) 65 (c) 107 (d) 71
  23. 23.What is the average of 55, 49, 33, 43, 48 and 24? (a) 43 (b) 42 (c) 44 (d) 41
  24. 24.What is the average of all the whole numbers from 43 to 65? (a) 11 (b) 54 (c) 55 (d) 22
  25. 25.A batter has an average of 51 runs in 4 matches. How many runs are needed in the next match to raise the average to 56? (a) 25 (b) 76 (c) 56 (d) 61
  26. 26.The average of 5 numbers is 18. When one number is taken away, the average of the rest is 21. Which number was taken away? (a) 7 (b) 18 (c) 39 (d) 6
  27. 27.A batter has an average of 55 runs in 8 matches. How many runs are needed in the next match to raise the average to 63? (a) 127 (b) 63 (c) 71 (d) 72
  28. 28.What is the average of 33, 32, 42, 47, 43 and 79? (a) 47 (b) 45 (c) 48 (d) 46
  29. 29.What is the average of 24, 17, 32, 26, 14 and 55? (a) 29 (b) 30 (c) 27 (d) 28
  30. 30.What is the average of all the whole numbers from 12 to 38? (a) 25 (b) 26 (c) 24 (d) 13
  31. 31.What is the average of 29, 26, 27, 46, 43 and 21? (a) 31 (b) 32 (c) 33 (d) 34
  32. 32.What is the average of 31, 36, 20, 43 and 30? (a) 31 (b) 40 (c) 33 (d) 32
  33. 33.A batter has an average of 55 runs in 3 matches. How many runs are needed in the next match to raise the average to 57? (a) 57 (b) 59 (c) 8 (d) 63
  34. 34.The average of 4 numbers is 36. When one number is taken away, the average of the rest is 39. Which number was taken away? (a) 28 (b) 75 (c) 27 (d) 36
  35. 35.What is the average of 74, 47, 55, 57, 48 and 91? (a) 61 (b) 64 (c) 62 (d) 63
  36. 36.The average of 5 numbers is 30. When one number is taken away, the average of the rest is 26. Which number was taken away? (a) 56 (b) 20 (c) 46 (d) 30
  37. 37.What is the average of all the whole numbers from 29 to 69? (a) 50 (b) 40 (c) 20 (d) 49
  38. 38.What is the average of 46, 51, 47, 56, 43 and 63? (a) 50 (b) 51 (c) 52 (d) 53
  39. 39.The average of 8 numbers is 28. When one number is taken away, the average of the rest is 23. Which number was taken away? (a) 63 (b) 40 (c) 51 (d) 28
  40. 40.What is the average of all the whole numbers from 14 to 48? (a) 32 (b) 31 (c) 17 (d) 34

Answer key

  1. 15
  2. 60
  3. 51
  4. 59
  5. 75
  6. 65
  7. 40
  8. 22
  9. 23
  10. 58
  11. 27
  12. 50
  13. 52
  14. 30
  15. 9
  16. 34
  17. 55
  18. 68
  19. 15
  20. 64
  21. 34
  22. 107
  23. 42
  24. 54
  25. 76
  26. 6
  27. 127
  28. 46
  29. 28
  30. 25
  31. 32
  32. 32
  33. 63
  34. 27
  35. 62
  36. 46
  37. 49
  38. 51
  39. 63
  40. 31

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