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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 307 · 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 4 numbers is 43. When one number is taken away, the average of the rest is 44. Which number was taken away? (a) 87 (b) 43 (c) 41 (d) 40
  2. 2.The average of 5 numbers is 42. When one number is taken away, the average of the rest is 46. Which number was taken away? (a) 88 (b) 42 (c) 26 (d) 27
  3. 3.The average of 7 numbers is 40. When one number is taken away, the average of the rest is 37. Which number was taken away? (a) 77 (b) 40 (c) 58 (d) 21
  4. 4.The average of 5 numbers is 12. When one number is taken away, the average of the rest is 11. Which number was taken away? (a) 12 (b) 23 (c) 5 (d) 16
  5. 5.What is the average of 68, 65, 50, 53, 63 and 37? (a) 57 (b) 58 (c) 55 (d) 56
  6. 6.What is the average of 69, 75, 72, 72, 77 and 103? (a) 80 (b) 77 (c) 78 (d) 79
  7. 7.What is the average of all the whole numbers from 53 to 69? (a) 62 (b) 8 (c) 61 (d) 16
  8. 8.What is the average of all the whole numbers from 18 to 48? (a) 30 (b) 34 (c) 33 (d) 15
  9. 9.A batter has an average of 49 runs in 7 matches. How many runs are needed in the next match to raise the average to 51? (a) 53 (b) 65 (c) 16 (d) 51
  10. 10.What is the average of all the whole numbers from 30 to 38? (a) 35 (b) 8 (c) 4 (d) 34
  11. 11.The average of 4 numbers is 43. When one number is taken away, the average of the rest is 38. Which number was taken away? (a) 58 (b) 20 (c) 43 (d) 81
  12. 12.What is the average of 13, 22, 25, 25 and 45? (a) 27 (b) 26 (c) 25 (d) 28
  13. 13.A batter has an average of 52 runs in 3 matches. How many runs are needed in the next match to raise the average to 55? (a) 12 (b) 64 (c) 58 (d) 55
  14. 14.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 28? (a) 28 (b) 56 (c) 35 (d) 77
  15. 15.The average of 6 numbers is 38. When one number is taken away, the average of the rest is 40. Which number was taken away? (a) 38 (b) 78 (c) 29 (d) 28
  16. 16.The average of 6 numbers is 47. When one number is taken away, the average of the rest is 52. Which number was taken away? (a) 23 (b) 99 (c) 22 (d) 47
  17. 17.The average of 4 numbers is 15. When one number is taken away, the average of the rest is 11. Which number was taken away? (a) 27 (b) 16 (c) 15 (d) 26
  18. 18.What is the average of all the whole numbers from 15 to 31? (a) 23 (b) 8 (c) 16 (d) 24
  19. 19.What is the average of 19, 20, 45, 25, 32 and 51? (a) 32 (b) 31 (c) 33 (d) 34
  20. 20.What is the average of 56, 78, 66, 48 and 67? (a) 62 (b) 63 (c) 64 (d) 65
  21. 21.What is the average of 42, 63, 57, 61 and 32? (a) 52 (b) 53 (c) 51 (d) 50
  22. 22.A batter has an average of 39 runs in 8 matches. How many runs are needed in the next match to raise the average to 47? (a) 72 (b) 55 (c) 47 (d) 111
  23. 23.A batter has an average of 53 runs in 3 matches. How many runs are needed in the next match to raise the average to 57? (a) 57 (b) 61 (c) 69 (d) 16
  24. 24.What is the average of all the whole numbers from 45 to 53? (a) 8 (b) 4 (c) 49 (d) 50
  25. 25.What is the average of all the whole numbers from 45 to 83? (a) 65 (b) 64 (c) 38 (d) 19
  26. 26.A batter has an average of 20 runs in 6 matches. How many runs are needed in the next match to raise the average to 23? (a) 23 (b) 21 (c) 26 (d) 41
  27. 27.What is the average of all the whole numbers from 23 to 41? (a) 18 (b) 9 (c) 32 (d) 33
  28. 28.A batter has an average of 33 runs in 9 matches. How many runs are needed in the next match to raise the average to 39? (a) 45 (b) 60 (c) 93 (d) 39
  29. 29.What is the average of all the whole numbers from 54 to 72? (a) 18 (b) 64 (c) 63 (d) 9
  30. 30.A batter has an average of 43 runs in 6 matches. How many runs are needed in the next match to raise the average to 45? (a) 45 (b) 47 (c) 57 (d) 14
  31. 31.A batter has an average of 32 runs in 6 matches. How many runs are needed in the next match to raise the average to 35? (a) 38 (b) 53 (c) 35 (d) 21
  32. 32.A batter has an average of 45 runs in 4 matches. How many runs are needed in the next match to raise the average to 49? (a) 20 (b) 53 (c) 65 (d) 49
  33. 33.The average of 5 numbers is 25. When one number is taken away, the average of the rest is 21. Which number was taken away? (a) 20 (b) 25 (c) 46 (d) 41
  34. 34.What is the average of all the whole numbers from 44 to 74? (a) 30 (b) 15 (c) 60 (d) 59
  35. 35.What is the average of all the whole numbers from 33 to 57? (a) 45 (b) 12 (c) 46 (d) 24
  36. 36.What is the average of 77, 63, 77, 58 and 70? (a) 70 (b) 69 (c) 71 (d) 68
  37. 37.The average of 5 numbers is 45. When one number is taken away, the average of the rest is 43. Which number was taken away? (a) 45 (b) 88 (c) 10 (d) 53
  38. 38.What is the average of all the whole numbers from 19 to 37? (a) 29 (b) 28 (c) 18 (d) 9
  39. 39.What is the average of all the whole numbers from 27 to 61? (a) 17 (b) 44 (c) 45 (d) 34
  40. 40.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 45? (a) 54 (b) 45 (c) 12 (d) 48

Answer key

  1. 40
  2. 26
  3. 58
  4. 16
  5. 56
  6. 78
  7. 61
  8. 33
  9. 65
  10. 34
  11. 58
  12. 26
  13. 64
  14. 77
  15. 28
  16. 22
  17. 27
  18. 23
  19. 32
  20. 63
  21. 51
  22. 111
  23. 69
  24. 49
  25. 64
  26. 41
  27. 32
  28. 93
  29. 63
  30. 57
  31. 53
  32. 65
  33. 41
  34. 59
  35. 45
  36. 69
  37. 53
  38. 28
  39. 44
  40. 54

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