AMC 8 Challenge Lab
Lesson 11: Statistics, Averages & Data Interpretation
Recognize • Model • Solve • Verify
50 original AMC 8-style multiple-choice problems with complete English solutions.
AMC 8 Strategy
Build speed without sacrificing accuracy.
1. Read for the exact target and hidden restrictions.
2. Translate words into a diagram, equation, table, or smaller case.
3. Estimate before calculating; eliminate impossible choices.
4. Look for shortcuts: symmetry, factoring, parity, ratios, or patterns.
5. Verify the result and make sure it answers the question asked.
Lesson Focus
Statistics, Averages & Data Interpretation
• Concept recognition
• Efficient contest strategy
• Mental-math checks
• Multiple representations
• Answer-choice verification
Practice 1-2
Choose the best answer. Solutions begin after Question 50.
1. The average of 10, 15, 23 and x is 18. What is x?��A. 20 B. 16 C. 24 D. 28 E. 18
2. What is 30% of 200?��A. 170 B. 55 C. 60 D. 6 E. 70
Practice 3-4
Choose the best answer. Solutions begin after Question 50.
3. There are 7 shirt choices, 7 pants choices and 3 hat choices. How many outfits are possible?��A. 150 B. 147 C. 144 D. 17 E. 49
4. The arithmetic sequence starts 2, 6, 10, ... . What is the 8th term?��A. 32 B. 30 C. 35 D. 34 E. 26
Practice 5-6
Choose the best answer. Solutions begin after Question 50.
5. If 5x+2=22, what is x?��A. 4 B. 3 C. 7 D. 5 E. 9
6. The average of 15, 16, 22 and x is 18. What is x?��A. 18 B. 17 C. 19 D. 15 E. 23
Practice 7-8
Choose the best answer. Solutions begin after Question 50.
7. What is 30% of 140?��A. 42 B. 37 C. 110 D. 4 E. 52
8. There are 7 shirt choices, 4 pants choices and 2 hat choices. How many outfits are possible?��A. 28 B. 56 C. 13 D. 58 E. 54
Practice 9-10
Choose the best answer. Solutions begin after Question 50.
9. The arithmetic sequence starts 2, 5, 8, ... . What is the 13th term?��A. 41 B. 38 C. 39 D. 35 E. 43
10. If 4x+7=43, what is x?��A. 14 B. 9 C. 8 D. 11 E. 10
Practice 11-12
Choose the best answer. Solutions begin after Question 50.
11. The average of 13, 17, 21 and x is 18. What is x?��A. 18 B. 21 C. 26 D. 17 E. 25
12. What is 30% of 80?��A. 2 B. 34 C. 50 D. 24 E. 19
Practice 13-14
Choose the best answer. Solutions begin after Question 50.
13. There are 7 shirt choices, 5 pants choices and 4 hat choices. How many outfits are possible?��A. 140 B. 16 C. 136 D. 144 E. 35
14. The arithmetic sequence starts 2, 4, 6, ... . What is the 10th term?��A. 22 B. 18 C. 24 D. 25 E. 20
Practice 15-16
Choose the best answer. Solutions begin after Question 50.
15. If 3x+4=16, what is x?��A. 7 B. 9 C. 4 D. 3 E. 5
16. The average of 11, 18, 20 and x is 18. What is x?��A. 27 B. 23 C. 18 D. 19 E. 16
Practice 17-18
Choose the best answer. Solutions begin after Question 50.
17. What is 30% of 180?��A. 150 B. 49 C. 64 D. 6 E. 54
18. There are 7 shirt choices, 6 pants choices and 3 hat choices. How many outfits are possible?��A. 123 B. 16 C. 126 D. 129 E. 42
Practice 19-20
Choose the best answer. Solutions begin after Question 50.
19. The arithmetic sequence starts 2, 9, 16, ... . What is the 15th term?��A. 100 B. 93 C. 107 D. 105 E. 105
20. If 2x+1=19, what is x?��A. 8 B. 14 C. 10 D. 3 E. 9
Practice 21-22
Choose the best answer. Solutions begin after Question 50.
21. The average of 16, 19, 19 and x is 18. What is x?��A. 22 B. 14 C. 22 D. 23 E. 18
22. What is 30% of 120?��A. 36 B. 31 C. 90 D. 46 E. 4
Practice 23-24
Choose the best answer. Solutions begin after Question 50.
23. There are 7 shirt choices, 7 pants choices and 2 hat choices. How many outfits are possible?��A. 49 B. 98 C. 96 D. 16 E. 100
24. The arithmetic sequence starts 2, 8, 14, ... . What is the 12th term?��A. 68 B. 72 C. 62 D. 73 E. 74
Practice 25-26
Choose the best answer. Solutions begin after Question 50.
25. If 7x+6=34, what is x?��A. 9 B. 13 C. 3 D. 4 E. 5
26. The average of 14, 20, 18 and x is 18. What is x?��A. 16 B. 20 C. 18 D. 17 E. 24
Practice 27-28
Choose the best answer. Solutions begin after Question 50.
27. What is 30% of 220?��A. 190 B. 61 C. 66 D. 7 E. 76
28. There are 7 shirt choices, 4 pants choices and 4 hat choices. How many outfits are possible?��A. 112 B. 15 C. 108 D. 28 E. 116
Practice 29-30
Choose the best answer. Solutions begin after Question 50.
29. The arithmetic sequence starts 2, 7, 12, ... . What is the 9th term?��A. 47 B. 45 C. 42 D. 47 E. 37
30. If 6x+3=57, what is x?��A. 10 B. 13 C. 9 D. 14 E. 8
Practice 31-32
Choose the best answer. Solutions begin after Question 50.
31. The average of 12, 21, 23 and x is 18. What is x?��A. 21 B. 16 C. 20 D. 12 E. 18
32. What is 30% of 160?��A. 58 B. 43 C. 48 D. 5 E. 130
Practice 33-34
Choose the best answer. Solutions begin after Question 50.
33. There are 7 shirt choices, 5 pants choices and 3 hat choices. How many outfits are possible?��A. 35 B. 108 C. 105 D. 102 E. 15
34. The arithmetic sequence starts 2, 6, 10, ... . What is the 14th term?��A. 59 B. 50 C. 54 D. 56 E. 58
Practice 35-36
Choose the best answer. Solutions begin after Question 50.
35. If 5x+8=28, what is x?��A. 4 B. 5 C. 13 D. 3 E. 9
36. The average of 10, 22, 22 and x is 18. What is x?��A. 22 B. 22 C. 18 D. 14 E. 23
Practice 37-38
Choose the best answer. Solutions begin after Question 50.
37. What is 30% of 100?��A. 30 B. 25 C. 40 D. 3 E. 70
38. There are 7 shirt choices, 6 pants choices and 2 hat choices. How many outfits are possible?��A. 84 B. 42 C. 86 D. 82 E. 15
Practice 39-40
Choose the best answer. Solutions begin after Question 50.
39. The arithmetic sequence starts 2, 5, 8, ... . What is the 11th term?��A. 32 B. 37 C. 35 D. 29 E. 33
40. If 4x+5=41, what is x?��A. 9 B. 14 C. 13 D. 10 E. 8
Practice 41-42
Choose the best answer. Solutions begin after Question 50.
41. The average of 15, 14, 21 and x is 18. What is x?��A. 27 B. 16 C. 22 D. 18 E. 26
42. What is 30% of 200?��A. 70 B. 55 C. 6 D. 170 E. 60
Practice 43-44
Choose the best answer. Solutions begin after Question 50.
43. There are 7 shirt choices, 7 pants choices and 4 hat choices. How many outfits are possible?��A. 196 B. 200 C. 18 D. 192 E. 49
44. The arithmetic sequence starts 2, 4, 6, ... . What is the 8th term?��A. 14 B. 21 C. 16 D. 20 E. 18
Practice 45-46
Choose the best answer. Solutions begin after Question 50.
45. If 3x+2=14, what is x?��A. 8 B. 5 C. 4 D. 3 E. 9
46. The average of 13, 15, 20 and x is 18. What is x?��A. 20 B. 24 C. 28 D. 16 E. 18
Practice 47-48
Choose the best answer. Solutions begin after Question 50.
47. What is 30% of 140?��A. 42 B. 37 C. 52 D. 4 E. 110
48. There are 7 shirt choices, 4 pants choices and 3 hat choices. How many outfits are possible?��A. 87 B. 14 C. 81 D. 28 E. 84
Practice 49-50
Choose the best answer. Solutions begin after Question 50.
49. The arithmetic sequence starts 2, 9, 16, ... . What is the 13th term?��A. 91 B. 86 C. 79 D. 93 E. 91
50. If 2x+7=25, what is x?��A. 14 B. 12 C. 8 D. 10 E. 9
Answer Key
Questions 1-50
1. C�2. C�3. B�4. B�5. A�6. C�7. A�8. B�9. B�10. B
11. B�12. D�13. A�14. E�15. C�16. B�17. E�18. C�19. A�20. E
21. E�22. A�23. B�24. A�25. D�26. B�27. C�28. A�29. C�30. C
31. B�32. C�33. C�34. C�35. A�36. C�37. A�38. A�39. A�40. A
41. C�42. E�43. A�44. C�45. C�46. B�47. A�48. E�49. B�50. E
Solutions 1-2
Check the method, not just the letter.
1. Answer: C. 24��The total must be 4×18=72. Subtract the known sum 48 to get x=24.
2. Answer: C. 60��30% of 200 = 30/100 × 200 = 60.
Solutions 3-4
Check the method, not just the letter.
3. Answer: B. 147��Multiplication principle: 7×7×3=147.
4. Answer: B. 30��a_n=a_1+(n−1)d=2+(8−1)(4)=30.
Solutions 5-6
Check the method, not just the letter.
5. Answer: A. 4��Subtract 2, then divide by 5: x=(22−2)/5=4.
6. Answer: C. 19��The total must be 4×18=72. Subtract the known sum 53 to get x=19.
Solutions 7-8
Check the method, not just the letter.
7. Answer: A. 42��30% of 140 = 30/100 × 140 = 42.
8. Answer: B. 56��Multiplication principle: 7×4×2=56.
Solutions 9-10
Check the method, not just the letter.
9. Answer: B. 38��a_n=a_1+(n−1)d=2+(13−1)(3)=38.
10. Answer: B. 9��Subtract 7, then divide by 4: x=(43−7)/4=9.
Solutions 11-12
Check the method, not just the letter.
11. Answer: B. 21��The total must be 4×18=72. Subtract the known sum 51 to get x=21.
12. Answer: D. 24��30% of 80 = 30/100 × 80 = 24.
Solutions 13-14
Check the method, not just the letter.
13. Answer: A. 140��Multiplication principle: 7×5×4=140.
14. Answer: E. 20��a_n=a_1+(n−1)d=2+(10−1)(2)=20.
Solutions 15-16
Check the method, not just the letter.
15. Answer: C. 4��Subtract 4, then divide by 3: x=(16−4)/3=4.
16. Answer: B. 23��The total must be 4×18=72. Subtract the known sum 49 to get x=23.
Solutions 17-18
Check the method, not just the letter.
17. Answer: E. 54��30% of 180 = 30/100 × 180 = 54.
18. Answer: C. 126��Multiplication principle: 7×6×3=126.
Solutions 19-20
Check the method, not just the letter.
19. Answer: A. 100��a_n=a_1+(n−1)d=2+(15−1)(7)=100.
20. Answer: E. 9��Subtract 1, then divide by 2: x=(19−1)/2=9.
Solutions 21-22
Check the method, not just the letter.
21. Answer: E. 18��The total must be 4×18=72. Subtract the known sum 54 to get x=18.
22. Answer: A. 36��30% of 120 = 30/100 × 120 = 36.
Solutions 23-24
Check the method, not just the letter.
23. Answer: B. 98��Multiplication principle: 7×7×2=98.
24. Answer: A. 68��a_n=a_1+(n−1)d=2+(12−1)(6)=68.
Solutions 25-26
Check the method, not just the letter.
25. Answer: D. 4��Subtract 6, then divide by 7: x=(34−6)/7=4.
26. Answer: B. 20��The total must be 4×18=72. Subtract the known sum 52 to get x=20.
Solutions 27-28
Check the method, not just the letter.
27. Answer: C. 66��30% of 220 = 30/100 × 220 = 66.
28. Answer: A. 112��Multiplication principle: 7×4×4=112.
Solutions 29-30
Check the method, not just the letter.
29. Answer: C. 42��a_n=a_1+(n−1)d=2+(9−1)(5)=42.
30. Answer: C. 9��Subtract 3, then divide by 6: x=(57−3)/6=9.
Solutions 31-32
Check the method, not just the letter.
31. Answer: B. 16��The total must be 4×18=72. Subtract the known sum 56 to get x=16.
32. Answer: C. 48��30% of 160 = 30/100 × 160 = 48.
Solutions 33-34
Check the method, not just the letter.
33. Answer: C. 105��Multiplication principle: 7×5×3=105.
34. Answer: C. 54��a_n=a_1+(n−1)d=2+(14−1)(4)=54.
Solutions 35-36
Check the method, not just the letter.
35. Answer: A. 4��Subtract 8, then divide by 5: x=(28−8)/5=4.
36. Answer: C. 18��The total must be 4×18=72. Subtract the known sum 54 to get x=18.
Solutions 37-38
Check the method, not just the letter.
37. Answer: A. 30��30% of 100 = 30/100 × 100 = 30.
38. Answer: A. 84��Multiplication principle: 7×6×2=84.
Solutions 39-40
Check the method, not just the letter.
39. Answer: A. 32��a_n=a_1+(n−1)d=2+(11−1)(3)=32.
40. Answer: A. 9��Subtract 5, then divide by 4: x=(41−5)/4=9.
Solutions 41-42
Check the method, not just the letter.
41. Answer: C. 22��The total must be 4×18=72. Subtract the known sum 50 to get x=22.
42. Answer: E. 60��30% of 200 = 30/100 × 200 = 60.
Solutions 43-44
Check the method, not just the letter.
43. Answer: A. 196��Multiplication principle: 7×7×4=196.
44. Answer: C. 16��a_n=a_1+(n−1)d=2+(8−1)(2)=16.
Solutions 45-46
Check the method, not just the letter.
45. Answer: C. 4��Subtract 2, then divide by 3: x=(14−2)/3=4.
46. Answer: B. 24��The total must be 4×18=72. Subtract the known sum 48 to get x=24.
Solutions 47-48
Check the method, not just the letter.
47. Answer: A. 42��30% of 140 = 30/100 × 140 = 42.
48. Answer: E. 84��Multiplication principle: 7×4×3=84.
Solutions 49-50
Check the method, not just the letter.
49. Answer: B. 86��a_n=a_1+(n−1)d=2+(13−1)(7)=86.
50. Answer: E. 9��Subtract 7, then divide by 2: x=(25−7)/2=9.