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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 95 · 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 46. When one number is taken away, the average of the rest is 51. Which number was taken away? (a) 22 (b) 97 (c) 21 (d) 46
  2. 2.A batter has an average of 35 runs in 5 matches. How many runs are needed in the next match to raise the average to 39? (a) 59 (b) 43 (c) 24 (d) 39
  3. 3.What is the average of all the whole numbers from 59 to 67? (a) 63 (b) 4 (c) 8 (d) 64
  4. 4.What is the average of 27, 51, 31, 30, 50 and 33? (a) 37 (b) 39 (c) 38 (d) 36
  5. 5.What is the average of all the whole numbers from 47 to 71? (a) 12 (b) 59 (c) 24 (d) 60
  6. 6.What is the average of 70, 72, 70, 52 and 71? (a) 66 (b) 68 (c) 67 (d) 69
  7. 7.A batter has an average of 51 runs in 3 matches. How many runs are needed in the next match to raise the average to 58? (a) 65 (b) 58 (c) 28 (d) 79
  8. 8.What is the average of all the whole numbers from 13 to 31? (a) 22 (b) 18 (c) 23 (d) 9
  9. 9.The average of 6 numbers is 34. When one number is taken away, the average of the rest is 38. Which number was taken away? (a) 72 (b) 15 (c) 34 (d) 14
  10. 10.What is the average of 31, 19, 31 and 35? (a) 28 (b) 29 (c) 30 (d) 31
  11. 11.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 46? (a) 46 (b) 74 (c) 35 (d) 53
  12. 12.What is the average of 57, 48, 44, 43 and 93? (a) 56 (b) 57 (c) 59 (d) 58
  13. 13.A batter has an average of 34 runs in 7 matches. How many runs are needed in the next match to raise the average to 39? (a) 40 (b) 39 (c) 44 (d) 74
  14. 14.The average of 8 numbers is 12. When one number is taken away, the average of the rest is 7. Which number was taken away? (a) 19 (b) 12 (c) 47 (d) 40
  15. 15.What is the average of all the whole numbers from 7 to 15? (a) 8 (b) 11 (c) 12 (d) 4
  16. 16.A batter has an average of 23 runs in 6 matches. How many runs are needed in the next match to raise the average to 25? (a) 27 (b) 37 (c) 25 (d) 14
  17. 17.What is the average of all the whole numbers from 48 to 86? (a) 19 (b) 38 (c) 67 (d) 68
  18. 18.What is the average of all the whole numbers from 26 to 64? (a) 19 (b) 38 (c) 45 (d) 46
  19. 19.What is the average of 52, 42, 28 and 26? (a) 37 (b) 36 (c) 39 (d) 38
  20. 20.A batter has an average of 34 runs in 6 matches. How many runs are needed in the next match to raise the average to 42? (a) 56 (b) 50 (c) 42 (d) 90
  21. 21.What is the average of all the whole numbers from 52 to 60? (a) 56 (b) 4 (c) 57 (d) 8
  22. 22.What is the average of 15, 39, 25 and 37? (a) 28 (b) 30 (c) 29 (d) 31
  23. 23.The average of 6 numbers is 21. When one number is taken away, the average of the rest is 20. Which number was taken away? (a) 6 (b) 41 (c) 21 (d) 26
  24. 24.A batter has an average of 56 runs in 7 matches. How many runs are needed in the next match to raise the average to 64? (a) 72 (b) 121 (c) 120 (d) 64
  25. 25.The average of 8 numbers is 35. When one number is taken away, the average of the rest is 34. Which number was taken away? (a) 35 (b) 8 (c) 42 (d) 69
  26. 26.A batter has an average of 21 runs in 4 matches. How many runs are needed in the next match to raise the average to 28? (a) 35 (b) 57 (c) 56 (d) 28
  27. 27.What is the average of 10, 22, 10, 6, 31 and 47? (a) 23 (b) 21 (c) 22 (d) 20
  28. 28.A batter has an average of 47 runs in 8 matches. How many runs are needed in the next match to raise the average to 52? (a) 57 (b) 45 (c) 52 (d) 92
  29. 29.What is the average of 64, 68, 68, 77 and 33? (a) 62 (b) 61 (c) 64 (d) 63
  30. 30.What is the average of 33, 24, 31, 47 and 35? (a) 33 (b) 36 (c) 34 (d) 35
  31. 31.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) 81 (b) 41 (c) 4 (d) 44
  32. 32.What is the average of 25, 45, 19, 38 and 23? (a) 30 (b) 32 (c) 29 (d) 31
  33. 33.What is the average of 9, 21, 24, 24, 17 and 37? (a) 21 (b) 22 (c) 24 (d) 23
  34. 34.The average of 5 numbers is 39. When one number is taken away, the average of the rest is 37. Which number was taken away? (a) 76 (b) 47 (c) 39 (d) 10
  35. 35.What is the average of 30, 21, 24, 26, 28 and 63? (a) 31 (b) 33 (c) 34 (d) 32
  36. 36.A batter has an average of 28 runs in 6 matches. How many runs are needed in the next match to raise the average to 33? (a) 63 (b) 35 (c) 33 (d) 38
  37. 37.What is the average of 55, 65, 78, 49, 62 and 69? (a) 63 (b) 64 (c) 65 (d) 62
  38. 38.What is the average of 77, 60, 79, 83, 85 and 42? (a) 72 (b) 70 (c) 73 (d) 71
  39. 39.What is the average of 36, 34, 14, 21, 28 and 35? (a) 30 (b) 29 (c) 28 (d) 27
  40. 40.The average of 6 numbers is 39. When one number is taken away, the average of the rest is 34. Which number was taken away? (a) 30 (b) 39 (c) 73 (d) 64

Answer key

  1. 21
  2. 59
  3. 63
  4. 37
  5. 59
  6. 67
  7. 79
  8. 22
  9. 14
  10. 29
  11. 74
  12. 57
  13. 74
  14. 47
  15. 11
  16. 37
  17. 67
  18. 45
  19. 37
  20. 90
  21. 56
  22. 29
  23. 26
  24. 120
  25. 42
  26. 56
  27. 21
  28. 92
  29. 62
  30. 34
  31. 44
  32. 30
  33. 22
  34. 47
  35. 32
  36. 63
  37. 63
  38. 71
  39. 28
  40. 64

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