Averages Worksheet for Maths Olympiad

Maths Olympiad topic 17: Averages · Set 934 · 40 questions

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.

1. 1.The average of 7 numbers is 42. When one number is taken away, the average of the rest is 41. Which number was taken away? (a) 83 (b) 42 (c) 7 (d) 48
2. 2.What is the average of all the whole numbers from 9 to 21? (a) 6 (b) 15 (c) 12 (d) 16
3. 3.What is the average of 40, 21, 28 and 15? (a) 25 (b) 28 (c) 27 (d) 26
4. 4.The average of 8 numbers is 46. When one number is taken away, the average of the rest is 47. Which number was taken away? (a) 93 (b) 39 (c) 40 (d) 46
5. 5.The average of 5 numbers is 46. When one number is taken away, the average of the rest is 45. Which number was taken away? (a) 46 (b) 50 (c) 5 (d) 91
6. 6.A batter has an average of 29 runs in 6 matches. How many runs are needed in the next match to raise the average to 36? (a) 78 (b) 49 (c) 43 (d) 36
7. 7.What is the average of all the whole numbers from 51 to 61? (a) 57 (b) 5 (c) 10 (d) 56
8. 8.The average of 4 numbers is 30. When one number is taken away, the average of the rest is 29. Which number was taken away? (a) 59 (b) 30 (c) 33 (d) 4
9. 9.The average of 7 numbers is 19. When one number is taken away, the average of the rest is 15. Which number was taken away? (a) 28 (b) 34 (c) 43 (d) 19
10. 10.What is the average of all the whole numbers from 7 to 45? (a) 38 (b) 19 (c) 26 (d) 27
11. 11.The average of 7 numbers is 38. When one number is taken away, the average of the rest is 41. Which number was taken away? (a) 38 (b) 20 (c) 21 (d) 79
12. 12.The average of 7 numbers is 20. When one number is taken away, the average of the rest is 16. Which number was taken away? (a) 20 (b) 44 (c) 36 (d) 28
13. 13.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) 26 (c) 41 (d) 21
14. 14.The average of 6 numbers is 31. When one number is taken away, the average of the rest is 28. Which number was taken away? (a) 46 (b) 59 (c) 18 (d) 31
15. 15.A batter has an average of 56 runs in 8 matches. How many runs are needed in the next match to raise the average to 62? (a) 62 (b) 54 (c) 68 (d) 110
16. 16.What is the average of all the whole numbers from 51 to 81? (a) 66 (b) 30 (c) 67 (d) 15
17. 17.The average of 8 numbers is 44. When one number is taken away, the average of the rest is 45. Which number was taken away? (a) 89 (b) 44 (c) 38 (d) 37
18. 18.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) 25 (b) 36 (c) 56 (d) 67
19. 19.What is the average of 36, 46, 51 and 31? (a) 43 (b) 41 (c) 40 (d) 42
20. 20.The average of 4 numbers is 40. When one number is taken away, the average of the rest is 37. Which number was taken away? (a) 77 (b) 12 (c) 49 (d) 40
21. 21.The average of 7 numbers is 44. When one number is taken away, the average of the rest is 43. Which number was taken away? (a) 7 (b) 87 (c) 44 (d) 50
22. 22.A batter has an average of 30 runs in 4 matches. How many runs are needed in the next match to raise the average to 38? (a) 38 (b) 46 (c) 70 (d) 40
23. 23.A batter has an average of 39 runs in 9 matches. How many runs are needed in the next match to raise the average to 47? (a) 119 (b) 47 (c) 55 (d) 80
24. 24.A batter has an average of 44 runs in 3 matches. How many runs are needed in the next match to raise the average to 50? (a) 68 (b) 24 (c) 50 (d) 56
25. 25.What is the average of 42, 26, 53, 27, 47 and 51? (a) 42 (b) 43 (c) 41 (d) 40
26. 26.The average of 7 numbers is 29. When one number is taken away, the average of the rest is 28. Which number was taken away? (a) 29 (b) 7 (c) 57 (d) 35
27. 27.What is the average of all the whole numbers from 28 to 44? (a) 37 (b) 16 (c) 36 (d) 8
28. 28.A batter has an average of 53 runs in 4 matches. How many runs are needed in the next match to raise the average to 60? (a) 88 (b) 35 (c) 60 (d) 67
29. 29.The average of 5 numbers is 25. When one number is taken away, the average of the rest is 29. Which number was taken away? (a) 9 (b) 25 (c) 54 (d) 10
30. 30.A batter has an average of 38 runs in 7 matches. How many runs are needed in the next match to raise the average to 41? (a) 24 (b) 41 (c) 62 (d) 44
31. 31.The average of 5 numbers is 50. When one number is taken away, the average of the rest is 45. Which number was taken away? (a) 25 (b) 50 (c) 70 (d) 95
32. 32.What is the average of 75, 65, 88, 83 and 69? (a) 75 (b) 77 (c) 76 (d) 95
33. 33.A batter has an average of 28 runs in 3 matches. How many runs are needed in the next match to raise the average to 34? (a) 34 (b) 24 (c) 52 (d) 40
34. 34.The average of 6 numbers is 44. When one number is taken away, the average of the rest is 49. Which number was taken away? (a) 44 (b) 19 (c) 20 (d) 93
35. 35.What is the average of all the whole numbers from 19 to 25? (a) 3 (b) 6 (c) 22 (d) 23
36. 36.The average of 4 numbers is 23. When one number is taken away, the average of the rest is 24. Which number was taken away? (a) 23 (b) 47 (c) 21 (d) 20
37. 37.What is the average of all the whole numbers from 50 to 78? (a) 65 (b) 64 (c) 28 (d) 14
38. 38.The average of 6 numbers is 49. When one number is taken away, the average of the rest is 54. Which number was taken away? (a) 49 (b) 25 (c) 24 (d) 103
39. 39.A batter has an average of 27 runs in 5 matches. How many runs are needed in the next match to raise the average to 34? (a) 34 (b) 42 (c) 69 (d) 41
40. 40.The average of 7 numbers is 12. When one number is taken away, the average of the rest is 8. Which number was taken away? (a) 28 (b) 12 (c) 20 (d) 36

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