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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 995 · 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.A batter has an average of 21 runs in 6 matches. How many runs are needed in the next match to raise the average to 29? (a) 29 (b) 37 (c) 56 (d) 77
  2. 2.A batter has an average of 32 runs in 8 matches. How many runs are needed in the next match to raise the average to 38? (a) 38 (b) 44 (c) 54 (d) 86
  3. 3.What is the average of 27, 32, 35, 51, 31 and 46? (a) 38 (b) 36 (c) 37 (d) 39
  4. 4.What is the average of 63, 77, 72, 67, 92 and 97? (a) 78 (b) 80 (c) 79 (d) 77
  5. 5.What is the average of all the whole numbers from 33 to 39? (a) 6 (b) 37 (c) 36 (d) 3
  6. 6.What is the average of all the whole numbers from 14 to 30? (a) 23 (b) 22 (c) 8 (d) 16
  7. 7.A batter has an average of 46 runs in 7 matches. How many runs are needed in the next match to raise the average to 49? (a) 49 (b) 70 (c) 24 (d) 52
  8. 8.The average of 5 numbers is 25. When one number is taken away, the average of the rest is 22. Which number was taken away? (a) 15 (b) 47 (c) 25 (d) 37
  9. 9.What is the average of 54, 50, 44, 36 and 51? (a) 49 (b) 48 (c) 46 (d) 47
  10. 10.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 52? (a) 56 (b) 52 (c) 32 (d) 80
  11. 11.What is the average of all the whole numbers from 56 to 78? (a) 67 (b) 11 (c) 68 (d) 22
  12. 12.A batter has an average of 21 runs in 6 matches. How many runs are needed in the next match to raise the average to 23? (a) 23 (b) 25 (c) 14 (d) 35
  13. 13.The average of 8 numbers is 42. When one number is taken away, the average of the rest is 46. Which number was taken away? (a) 42 (b) 15 (c) 88 (d) 14
  14. 14.What is the average of all the whole numbers from 13 to 19? (a) 16 (b) 6 (c) 3 (d) 17
  15. 15.The average of 4 numbers is 43. When one number is taken away, the average of the rest is 44. Which number was taken away? (a) 41 (b) 40 (c) 43 (d) 87
  16. 16.The average of 6 numbers is 32. When one number is taken away, the average of the rest is 33. Which number was taken away? (a) 28 (b) 65 (c) 27 (d) 32
  17. 17.What is the average of all the whole numbers from 29 to 41? (a) 35 (b) 36 (c) 6 (d) 12
  18. 18.What is the average of 17, 30, 19, 15 and 34? (a) 24 (b) 22 (c) 25 (d) 23
  19. 19.The average of 8 numbers is 37. When one number is taken away, the average of the rest is 39. Which number was taken away? (a) 37 (b) 23 (c) 76 (d) 24
  20. 20.The average of 7 numbers is 12. When one number is taken away, the average of the rest is 10. Which number was taken away? (a) 22 (b) 14 (c) 24 (d) 12
  21. 21.What is the average of 47, 50, 35, 32 and 56? (a) 43 (b) 45 (c) 55 (d) 44
  22. 22.What is the average of 60, 89, 69, 62, 85 and 79? (a) 73 (b) 75 (c) 76 (d) 74
  23. 23.What is the average of 27, 39, 14, 14 and 36? (a) 27 (b) 28 (c) 25 (d) 26
  24. 24.The average of 8 numbers is 18. When one number is taken away, the average of the rest is 17. Which number was taken away? (a) 8 (b) 35 (c) 18 (d) 25
  25. 25.What is the average of 88, 88, 62, 63 and 79? (a) 75 (b) 77 (c) 95 (d) 76
  26. 26.What is the average of all the whole numbers from 30 to 38? (a) 35 (b) 8 (c) 4 (d) 34
  27. 27.The average of 6 numbers is 20. When one number is taken away, the average of the rest is 17. Which number was taken away? (a) 20 (b) 37 (c) 35 (d) 18
  28. 28.A batter has an average of 28 runs in 4 matches. How many runs are needed in the next match to raise the average to 36? (a) 68 (b) 40 (c) 36 (d) 44
  29. 29.What is the average of 82, 72, 67, 75, 77 and 47? (a) 70 (b) 84 (c) 71 (d) 69
  30. 30.What is the average of 40, 17, 22, 19, 27 and 37? (a) 28 (b) 26 (c) 29 (d) 27
  31. 31.The average of 7 numbers is 18. When one number is taken away, the average of the rest is 19. Which number was taken away? (a) 13 (b) 12 (c) 37 (d) 18
  32. 32.A batter has an average of 31 runs in 4 matches. How many runs are needed in the next match to raise the average to 38? (a) 35 (b) 38 (c) 66 (d) 45
  33. 33.The average of 8 numbers is 17. When one number is taken away, the average of the rest is 19. Which number was taken away? (a) 4 (b) 3 (c) 17 (d) 36
  34. 34.What is the average of 20, 35, 29 and 36? (a) 29 (b) 30 (c) 40 (d) 31
  35. 35.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 47? (a) 62 (b) 52 (c) 20 (d) 47
  36. 36.The average of 4 numbers is 22. When one number is taken away, the average of the rest is 17. Which number was taken away? (a) 22 (b) 39 (c) 37 (d) 20
  37. 37.A batter has an average of 27 runs in 8 matches. How many runs are needed in the next match to raise the average to 33? (a) 33 (b) 81 (c) 54 (d) 39
  38. 38.The average of 5 numbers is 26. When one number is taken away, the average of the rest is 21. Which number was taken away? (a) 25 (b) 46 (c) 47 (d) 26
  39. 39.A batter has an average of 21 runs in 7 matches. How many runs are needed in the next match to raise the average to 23? (a) 23 (b) 37 (c) 16 (d) 25
  40. 40.The average of 7 numbers is 41. When one number is taken away, the average of the rest is 43. Which number was taken away? (a) 41 (b) 84 (c) 29 (d) 30

Answer key

  1. 77
  2. 86
  3. 37
  4. 78
  5. 36
  6. 22
  7. 70
  8. 37
  9. 47
  10. 80
  11. 67
  12. 35
  13. 14
  14. 16
  15. 40
  16. 27
  17. 35
  18. 23
  19. 23
  20. 24
  21. 44
  22. 74
  23. 26
  24. 25
  25. 76
  26. 34
  27. 35
  28. 68
  29. 70
  30. 27
  31. 12
  32. 66
  33. 3
  34. 30
  35. 62
  36. 37
  37. 81
  38. 46
  39. 37
  40. 29

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