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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 149 · 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 38. When one number is taken away, the average of the rest is 43. Which number was taken away? (a) 8 (b) 81 (c) 9 (d) 38
  2. 2.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 34? (a) 42 (b) 70 (c) 34 (d) 40
  3. 3.A batter has an average of 37 runs in 5 matches. How many runs are needed in the next match to raise the average to 39? (a) 12 (b) 41 (c) 39 (d) 49
  4. 4.The average of 5 numbers is 31. When one number is taken away, the average of the rest is 35. Which number was taken away? (a) 16 (b) 31 (c) 66 (d) 15
  5. 5.The average of 5 numbers is 26. When one number is taken away, the average of the rest is 23. Which number was taken away? (a) 49 (b) 26 (c) 15 (d) 38
  6. 6.What is the average of 56, 56, 82 and 74? (a) 68 (b) 66 (c) 69 (d) 67
  7. 7.The average of 7 numbers is 21. When one number is taken away, the average of the rest is 16. Which number was taken away? (a) 35 (b) 21 (c) 37 (d) 51
  8. 8.What is the average of 11, 29, 38 and 26? (a) 26 (b) 25 (c) 27 (d) 28
  9. 9.What is the average of all the whole numbers from 18 to 42? (a) 24 (b) 30 (c) 31 (d) 12
  10. 10.What is the average of 70, 61, 83 and 58? (a) 68 (b) 69 (c) 67 (d) 70
  11. 11.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 61? (a) 61 (b) 68 (c) 56 (d) 110
  12. 12.A batter has an average of 57 runs in 9 matches. How many runs are needed in the next match to raise the average to 60? (a) 30 (b) 87 (c) 60 (d) 63
  13. 13.A batter has an average of 48 runs in 7 matches. How many runs are needed in the next match to raise the average to 50? (a) 52 (b) 64 (c) 16 (d) 50
  14. 14.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) 69 (b) 15 (c) 16 (d) 33
  15. 15.A batter has an average of 33 runs in 4 matches. How many runs are needed in the next match to raise the average to 36? (a) 36 (b) 15 (c) 48 (d) 39
  16. 16.What is the average of all the whole numbers from 18 to 52? (a) 34 (b) 17 (c) 35 (d) 36
  17. 17.The average of 4 numbers is 35. When one number is taken away, the average of the rest is 40. Which number was taken away? (a) 21 (b) 20 (c) 35 (d) 75
  18. 18.What is the average of all the whole numbers from 29 to 41? (a) 36 (b) 6 (c) 12 (d) 35
  19. 19.A batter has an average of 53 runs in 9 matches. How many runs are needed in the next match to raise the average to 56? (a) 83 (b) 30 (c) 56 (d) 59
  20. 20.A batter has an average of 24 runs in 3 matches. How many runs are needed in the next match to raise the average to 31? (a) 38 (b) 31 (c) 28 (d) 52
  21. 21.A batter has an average of 59 runs in 8 matches. How many runs are needed in the next match to raise the average to 67? (a) 67 (b) 75 (c) 72 (d) 131
  22. 22.The average of 7 numbers is 50. When one number is taken away, the average of the rest is 51. Which number was taken away? (a) 45 (b) 50 (c) 44 (d) 101
  23. 23.What is the average of 29, 32, 11, 33, 15 and 6? (a) 22 (b) 20 (c) 23 (d) 21
  24. 24.A batter has an average of 55 runs in 6 matches. How many runs are needed in the next match to raise the average to 58? (a) 76 (b) 21 (c) 58 (d) 61
  25. 25.The average of 6 numbers is 27. When one number is taken away, the average of the rest is 29. Which number was taken away? (a) 18 (b) 56 (c) 17 (d) 27
  26. 26.The average of 5 numbers is 23. When one number is taken away, the average of the rest is 27. Which number was taken away? (a) 8 (b) 50 (c) 23 (d) 7
  27. 27.A batter has an average of 29 runs in 5 matches. How many runs are needed in the next match to raise the average to 35? (a) 35 (b) 36 (c) 65 (d) 41
  28. 28.The average of 6 numbers is 46. When one number is taken away, the average of the rest is 49. Which number was taken away? (a) 95 (b) 46 (c) 32 (d) 31
  29. 29.What is the average of all the whole numbers from 48 to 62? (a) 14 (b) 56 (c) 55 (d) 7
  30. 30.What is the average of all the whole numbers from 59 to 83? (a) 12 (b) 71 (c) 72 (d) 24
  31. 31.What is the average of 28, 41, 54, 41, 33 and 55? (a) 43 (b) 41 (c) 44 (d) 42
  32. 32.A batter has an average of 44 runs in 9 matches. How many runs are needed in the next match to raise the average to 52? (a) 60 (b) 52 (c) 124 (d) 80
  33. 33.What is the average of all the whole numbers from 52 to 64? (a) 12 (b) 6 (c) 58 (d) 59
  34. 34.What is the average of 59, 64, 60, 62, 63 and 118? (a) 73 (b) 70 (c) 72 (d) 71
  35. 35.What is the average of 52, 67, 70 and 51? (a) 80 (b) 61 (c) 59 (d) 60
  36. 36.The average of 7 numbers is 16. When one number is taken away, the average of the rest is 17. Which number was taken away? (a) 11 (b) 16 (c) 10 (d) 33
  37. 37.The average of 7 numbers is 45. When one number is taken away, the average of the rest is 44. Which number was taken away? (a) 45 (b) 51 (c) 89 (d) 7
  38. 38.A batter has an average of 20 runs in 5 matches. How many runs are needed in the next match to raise the average to 22? (a) 24 (b) 12 (c) 32 (d) 22
  39. 39.What is the average of 22, 32, 26 and 28? (a) 26 (b) 28 (c) 36 (d) 27
  40. 40.A batter has an average of 25 runs in 9 matches. How many runs are needed in the next match to raise the average to 29? (a) 40 (b) 29 (c) 65 (d) 33

Answer key

  1. 8
  2. 70
  3. 49
  4. 15
  5. 38
  6. 67
  7. 51
  8. 26
  9. 30
  10. 68
  11. 110
  12. 87
  13. 64
  14. 15
  15. 48
  16. 35
  17. 20
  18. 35
  19. 83
  20. 52
  21. 131
  22. 44
  23. 21
  24. 76
  25. 17
  26. 7
  27. 65
  28. 31
  29. 55
  30. 71
  31. 42
  32. 124
  33. 58
  34. 71
  35. 60
  36. 10
  37. 51
  38. 32
  39. 27
  40. 65

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