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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 267 · 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 25. When one number is taken away, the average of the rest is 26. Which number was taken away? (a) 25 (b) 20 (c) 51 (d) 19
  2. 2.What is the average of all the whole numbers from 18 to 58? (a) 38 (b) 20 (c) 40 (d) 39
  3. 3.The average of 8 numbers is 21. When one number is taken away, the average of the rest is 22. Which number was taken away? (a) 21 (b) 15 (c) 43 (d) 14
  4. 4.What is the average of 37, 39, 17, 22 and 45? (a) 40 (b) 33 (c) 31 (d) 32
  5. 5.The average of 7 numbers is 44. When one number is taken away, the average of the rest is 39. Which number was taken away? (a) 74 (b) 35 (c) 44 (d) 83
  6. 6.The average of 4 numbers is 32. When one number is taken away, the average of the rest is 28. Which number was taken away? (a) 32 (b) 16 (c) 44 (d) 60
  7. 7.What is the average of all the whole numbers from 24 to 44? (a) 20 (b) 10 (c) 35 (d) 34
  8. 8.The average of 6 numbers is 37. When one number is taken away, the average of the rest is 34. Which number was taken away? (a) 37 (b) 71 (c) 18 (d) 52
  9. 9.The average of 4 numbers is 17. When one number is taken away, the average of the rest is 14. Which number was taken away? (a) 12 (b) 26 (c) 17 (d) 31
  10. 10.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 54? (a) 63 (b) 54 (c) 110 (d) 61
  11. 11.A batter has an average of 58 runs in 6 matches. How many runs are needed in the next match to raise the average to 63? (a) 68 (b) 35 (c) 93 (d) 63
  12. 12.The average of 5 numbers is 28. When one number is taken away, the average of the rest is 27. Which number was taken away? (a) 32 (b) 5 (c) 28 (d) 55
  13. 13.What is the average of all the whole numbers from 37 to 63? (a) 50 (b) 51 (c) 13 (d) 26
  14. 14.What is the average of 15, 29, 23 and 37? (a) 27 (b) 28 (c) 26 (d) 25
  15. 15.The average of 8 numbers is 42. When one number is taken away, the average of the rest is 37. Which number was taken away? (a) 40 (b) 79 (c) 77 (d) 42
  16. 16.What is the average of all the whole numbers from 55 to 95? (a) 40 (b) 20 (c) 75 (d) 76
  17. 17.What is the average of 52, 69, 73, 63 and 63? (a) 65 (b) 63 (c) 64 (d) 80
  18. 18.What is the average of 47, 45, 39 and 65? (a) 51 (b) 49 (c) 50 (d) 48
  19. 19.The average of 7 numbers is 10. When one number is taken away, the average of the rest is 7. Which number was taken away? (a) 10 (b) 21 (c) 17 (d) 28
  20. 20.The average of 6 numbers is 33. When one number is taken away, the average of the rest is 32. Which number was taken away? (a) 33 (b) 65 (c) 6 (d) 38
  21. 21.What is the average of 40, 39, 36, 43 and 77? (a) 48 (b) 46 (c) 49 (d) 47
  22. 22.What is the average of all the whole numbers from 58 to 72? (a) 7 (b) 65 (c) 66 (d) 14
  23. 23.What is the average of all the whole numbers from 28 to 40? (a) 6 (b) 34 (c) 35 (d) 12
  24. 24.What is the average of 81, 91, 75, 75, 65 and 69? (a) 77 (b) 78 (c) 76 (d) 75
  25. 25.A batter has an average of 23 runs in 7 matches. How many runs are needed in the next match to raise the average to 31? (a) 31 (b) 64 (c) 87 (d) 39
  26. 26.What is the average of 77, 83, 77, 64, 77 and 90? (a) 79 (b) 77 (c) 78 (d) 80
  27. 27.A batter has an average of 53 runs in 8 matches. How many runs are needed in the next match to raise the average to 57? (a) 61 (b) 36 (c) 89 (d) 57
  28. 28.What is the average of all the whole numbers from 16 to 48? (a) 33 (b) 32 (c) 16 (d) 31
  29. 29.A batter has an average of 31 runs in 6 matches. How many runs are needed in the next match to raise the average to 33? (a) 35 (b) 33 (c) 45 (d) 14
  30. 30.What is the average of 35, 14, 17, 18, 23 and 49? (a) 25 (b) 26 (c) 27 (d) 28
  31. 31.The average of 4 numbers is 43. When one number is taken away, the average of the rest is 48. Which number was taken away? (a) 91 (b) 43 (c) 28 (d) 29
  32. 32.What is the average of 49, 37, 62, 42 and 50? (a) 47 (b) 49 (c) 48 (d) 60
  33. 33.What is the average of 64, 81, 64, 88 and 78? (a) 77 (b) 75 (c) 76 (d) 74
  34. 34.A batter has an average of 30 runs in 5 matches. How many runs are needed in the next match to raise the average to 32? (a) 34 (b) 32 (c) 12 (d) 42
  35. 35.The average of 7 numbers is 22. When one number is taken away, the average of the rest is 25. Which number was taken away? (a) 47 (b) 5 (c) 22 (d) 4
  36. 36.The average of 4 numbers is 26. When one number is taken away, the average of the rest is 30. Which number was taken away? (a) 14 (b) 56 (c) 15 (d) 26
  37. 37.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 63? (a) 70 (b) 56 (c) 112 (d) 63
  38. 38.What is the average of 64, 47, 43 and 46? (a) 49 (b) 51 (c) 52 (d) 50
  39. 39.What is the average of all the whole numbers from 36 to 42? (a) 39 (b) 40 (c) 6 (d) 3
  40. 40.The average of 8 numbers is 23. When one number is taken away, the average of the rest is 24. Which number was taken away? (a) 23 (b) 16 (c) 47 (d) 17

Answer key

  1. 19
  2. 38
  3. 14
  4. 32
  5. 74
  6. 44
  7. 34
  8. 52
  9. 26
  10. 110
  11. 93
  12. 32
  13. 50
  14. 26
  15. 77
  16. 75
  17. 64
  18. 49
  19. 28
  20. 38
  21. 47
  22. 65
  23. 34
  24. 76
  25. 87
  26. 78
  27. 89
  28. 32
  29. 45
  30. 26
  31. 28
  32. 48
  33. 75
  34. 42
  35. 4
  36. 14
  37. 112
  38. 50
  39. 39
  40. 16

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