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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 231 · 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 31. When one number is taken away, the average of the rest is 29. Which number was taken away? (a) 31 (b) 14 (c) 60 (d) 43
  2. 2.What is the average of all the whole numbers from 9 to 41? (a) 32 (b) 25 (c) 26 (d) 16
  3. 3.The average of 6 numbers is 26. When one number is taken away, the average of the rest is 29. Which number was taken away? (a) 12 (b) 11 (c) 55 (d) 26
  4. 4.What is the average of all the whole numbers from 27 to 37? (a) 5 (b) 10 (c) 33 (d) 32
  5. 5.What is the average of 57, 79, 63, 81, 57 and 95? (a) 74 (b) 72 (c) 73 (d) 71
  6. 6.What is the average of all the whole numbers from 13 to 31? (a) 23 (b) 22 (c) 9 (d) 18
  7. 7.The average of 6 numbers is 42. When one number is taken away, the average of the rest is 39. Which number was taken away? (a) 81 (b) 18 (c) 42 (d) 57
  8. 8.A batter has an average of 59 runs in 9 matches. How many runs are needed in the next match to raise the average to 63? (a) 67 (b) 99 (c) 63 (d) 40
  9. 9.A batter has an average of 23 runs in 8 matches. How many runs are needed in the next match to raise the average to 26? (a) 27 (b) 26 (c) 50 (d) 29
  10. 10.What is the average of 81, 85, 91, 72 and 56? (a) 79 (b) 77 (c) 76 (d) 78
  11. 11.The average of 5 numbers is 50. When one number is taken away, the average of the rest is 46. Which number was taken away? (a) 96 (b) 50 (c) 20 (d) 66
  12. 12.What is the average of 28, 33, 44 and 39? (a) 48 (b) 37 (c) 35 (d) 36
  13. 13.A batter has an average of 49 runs in 6 matches. How many runs are needed in the next match to raise the average to 52? (a) 70 (b) 55 (c) 52 (d) 21
  14. 14.The average of 4 numbers is 10. When one number is taken away, the average of the rest is 12. Which number was taken away? (a) 10 (b) 4 (c) 22 (d) 5
  15. 15.The average of 4 numbers is 46. When one number is taken away, the average of the rest is 51. Which number was taken away? (a) 31 (b) 46 (c) 32 (d) 97
  16. 16.What is the average of 47, 60, 67, 70, 51 and 35? (a) 55 (b) 56 (c) 66 (d) 54
  17. 17.What is the average of 9, 16, 32, 22, 28 and 31? (a) 22 (b) 24 (c) 25 (d) 23
  18. 18.A batter has an average of 58 runs in 3 matches. How many runs are needed in the next match to raise the average to 60? (a) 62 (b) 60 (c) 8 (d) 66
  19. 19.What is the average of all the whole numbers from 9 to 37? (a) 14 (b) 28 (c) 24 (d) 23
  20. 20.The average of 5 numbers is 50. When one number is taken away, the average of the rest is 53. Which number was taken away? (a) 39 (b) 103 (c) 50 (d) 38
  21. 21.A batter has an average of 35 runs in 9 matches. How many runs are needed in the next match to raise the average to 43? (a) 115 (b) 43 (c) 51 (d) 80
  22. 22.A batter has an average of 42 runs in 3 matches. How many runs are needed in the next match to raise the average to 50? (a) 58 (b) 74 (c) 32 (d) 50
  23. 23.The average of 4 numbers is 29. When one number is taken away, the average of the rest is 28. Which number was taken away? (a) 57 (b) 29 (c) 32 (d) 4
  24. 24.A batter has an average of 59 runs in 6 matches. How many runs are needed in the next match to raise the average to 64? (a) 64 (b) 35 (c) 94 (d) 69
  25. 25.What is the average of all the whole numbers from 56 to 74? (a) 66 (b) 65 (c) 9 (d) 18
  26. 26.The average of 7 numbers is 32. When one number is taken away, the average of the rest is 33. Which number was taken away? (a) 32 (b) 26 (c) 27 (d) 65
  27. 27.What is the average of all the whole numbers from 28 to 46? (a) 38 (b) 37 (c) 18 (d) 9
  28. 28.The average of 7 numbers is 26. When one number is taken away, the average of the rest is 27. Which number was taken away? (a) 26 (b) 53 (c) 20 (d) 21
  29. 29.What is the average of 66, 77, 63, 55, 72 and 75? (a) 67 (b) 70 (c) 69 (d) 68
  30. 30.The average of 8 numbers is 32. When one number is taken away, the average of the rest is 28. Which number was taken away? (a) 61 (b) 32 (c) 59 (d) 60
  31. 31.The average of 4 numbers is 25. When one number is taken away, the average of the rest is 22. Which number was taken away? (a) 12 (b) 25 (c) 47 (d) 34
  32. 32.The average of 5 numbers is 12. When one number is taken away, the average of the rest is 8. Which number was taken away? (a) 28 (b) 20 (c) 12 (d) 29
  33. 33.A batter has an average of 39 runs in 4 matches. How many runs are needed in the next match to raise the average to 42? (a) 42 (b) 15 (c) 45 (d) 54
  34. 34.What is the average of all the whole numbers from 48 to 62? (a) 55 (b) 7 (c) 56 (d) 14
  35. 35.What is the average of 65, 70, 48, 65 and 67? (a) 63 (b) 62 (c) 65 (d) 64
  36. 36.The average of 8 numbers is 36. When one number is taken away, the average of the rest is 34. Which number was taken away? (a) 70 (b) 16 (c) 50 (d) 36
  37. 37.What is the average of 31, 26, 22, 33, 41 and 27? (a) 36 (b) 29 (c) 31 (d) 30
  38. 38.What is the average of 48, 59, 55, 76 and 72? (a) 61 (b) 62 (c) 63 (d) 64
  39. 39.What is the average of all the whole numbers from 20 to 46? (a) 13 (b) 26 (c) 34 (d) 33
  40. 40.A batter has an average of 57 runs in 7 matches. How many runs are needed in the next match to raise the average to 60? (a) 63 (b) 24 (c) 60 (d) 81

Answer key

  1. 43
  2. 25
  3. 11
  4. 32
  5. 72
  6. 22
  7. 57
  8. 99
  9. 50
  10. 77
  11. 66
  12. 36
  13. 70
  14. 4
  15. 31
  16. 55
  17. 23
  18. 66
  19. 23
  20. 38
  21. 115
  22. 74
  23. 32
  24. 94
  25. 65
  26. 26
  27. 37
  28. 20
  29. 68
  30. 60
  31. 34
  32. 28
  33. 54
  34. 55
  35. 63
  36. 50
  37. 30
  38. 62
  39. 33
  40. 81

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