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Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 75 · 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 20 runs in 7 matches. How many runs are needed in the next match to raise the average to 25? (a) 60 (b) 40 (c) 25 (d) 30
  2. 2.What is the average of 28, 35, 31 and 78? (a) 44 (b) 45 (c) 42 (d) 43
  3. 3.What is the average of 62, 51, 66, 55, 55 and 89? (a) 62 (b) 65 (c) 64 (d) 63
  4. 4.The average of 4 numbers is 26. When one number is taken away, the average of the rest is 29. Which number was taken away? (a) 55 (b) 17 (c) 26 (d) 18
  5. 5.What is the average of all the whole numbers from 38 to 52? (a) 14 (b) 46 (c) 45 (d) 7
  6. 6.A batter has an average of 57 runs in 7 matches. How many runs are needed in the next match to raise the average to 61? (a) 32 (b) 65 (c) 61 (d) 89
  7. 7.A batter has an average of 51 runs in 4 matches. How many runs are needed in the next match to raise the average to 53? (a) 61 (b) 53 (c) 10 (d) 55
  8. 8.The average of 8 numbers is 47. When one number is taken away, the average of the rest is 50. Which number was taken away? (a) 27 (b) 47 (c) 26 (d) 97
  9. 9.The average of 5 numbers is 36. When one number is taken away, the average of the rest is 31. Which number was taken away? (a) 67 (b) 25 (c) 36 (d) 56
  10. 10.What is the average of all the whole numbers from 7 to 47? (a) 20 (b) 27 (c) 28 (d) 40
  11. 11.What is the average of all the whole numbers from 21 to 33? (a) 28 (b) 27 (c) 6 (d) 12
  12. 12.A batter has an average of 30 runs in 8 matches. How many runs are needed in the next match to raise the average to 32? (a) 32 (b) 18 (c) 48 (d) 34
  13. 13.What is the average of all the whole numbers from 50 to 72? (a) 22 (b) 62 (c) 61 (d) 11
  14. 14.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 36? (a) 56 (b) 44 (c) 36 (d) 84
  15. 15.What is the average of 39, 31, 30, 39, 25 and 4? (a) 30 (b) 27 (c) 29 (d) 28
  16. 16.What is the average of all the whole numbers from 30 to 60? (a) 46 (b) 45 (c) 30 (d) 15
  17. 17.What is the average of all the whole numbers from 16 to 44? (a) 14 (b) 31 (c) 30 (d) 28
  18. 18.The average of 4 numbers is 49. When one number is taken away, the average of the rest is 54. Which number was taken away? (a) 103 (b) 35 (c) 49 (d) 34
  19. 19.What is the average of all the whole numbers from 52 to 58? (a) 3 (b) 56 (c) 6 (d) 55
  20. 20.The average of 8 numbers is 30. When one number is taken away, the average of the rest is 31. Which number was taken away? (a) 24 (b) 30 (c) 23 (d) 61
  21. 21.What is the average of all the whole numbers from 18 to 44? (a) 26 (b) 32 (c) 31 (d) 13
  22. 22.What is the average of 42, 24, 41, 53 and 35? (a) 41 (b) 38 (c) 39 (d) 40
  23. 23.What is the average of 77, 55, 53, 67 and 78? (a) 68 (b) 65 (c) 67 (d) 66
  24. 24.What is the average of all the whole numbers from 13 to 47? (a) 30 (b) 17 (c) 31 (d) 34
  25. 25.What is the average of all the whole numbers from 58 to 92? (a) 17 (b) 75 (c) 76 (d) 34
  26. 26.What is the average of all the whole numbers from 14 to 28? (a) 22 (b) 7 (c) 14 (d) 21
  27. 27.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) 37 (b) 13 (c) 18 (d) 12
  28. 28.What is the average of 70, 76, 73, 62 and 34? (a) 62 (b) 64 (c) 65 (d) 63
  29. 29.A batter has an average of 32 runs in 3 matches. How many runs are needed in the next match to raise the average to 38? (a) 24 (b) 56 (c) 44 (d) 38
  30. 30.A batter has an average of 35 runs in 7 matches. How many runs are needed in the next match to raise the average to 42? (a) 49 (b) 56 (c) 91 (d) 42
  31. 31.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) 24 (c) 14 (d) 12
  32. 32.A batter has an average of 22 runs in 4 matches. How many runs are needed in the next match to raise the average to 25? (a) 37 (b) 25 (c) 15 (d) 28
  33. 33.What is the average of 50, 39, 38, 34, 52 and 69? (a) 49 (b) 46 (c) 47 (d) 48
  34. 34.A batter has an average of 25 runs in 4 matches. How many runs are needed in the next match to raise the average to 33? (a) 65 (b) 40 (c) 33 (d) 41
  35. 35.What is the average of 40, 45, 53, 66 and 61? (a) 53 (b) 55 (c) 52 (d) 54
  36. 36.What is the average of all the whole numbers from 20 to 46? (a) 34 (b) 13 (c) 26 (d) 33
  37. 37.A batter has an average of 46 runs in 5 matches. How many runs are needed in the next match to raise the average to 49? (a) 49 (b) 52 (c) 18 (d) 64
  38. 38.What is the average of 36, 16, 12, 10, 9 and 43? (a) 23 (b) 22 (c) 21 (d) 20
  39. 39.The average of 6 numbers is 11. When one number is taken away, the average of the rest is 9. Which number was taken away? (a) 21 (b) 20 (c) 11 (d) 12
  40. 40.The average of 6 numbers is 10. When one number is taken away, the average of the rest is 7. Which number was taken away? (a) 17 (b) 25 (c) 18 (d) 10

Answer key

  1. 60
  2. 43
  3. 63
  4. 17
  5. 45
  6. 89
  7. 61
  8. 26
  9. 56
  10. 27
  11. 27
  12. 48
  13. 61
  14. 84
  15. 28
  16. 45
  17. 30
  18. 34
  19. 55
  20. 23
  21. 31
  22. 39
  23. 66
  24. 30
  25. 75
  26. 21
  27. 12
  28. 63
  29. 56
  30. 91
  31. 24
  32. 37
  33. 47
  34. 65
  35. 53
  36. 33
  37. 64
  38. 21
  39. 21
  40. 25

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