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AMC 8 Challenge Lab

Lesson 2: Fractions, Decimals, Percents & Ratios

Recognize • Model • Solve • Verify

50 original AMC 8-style multiple-choice problems with complete English solutions.

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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.

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Lesson Focus

Fractions, Decimals, Percents & Ratios

• Concept recognition

• Efficient contest strategy

• Mental-math checks

• Multiple representations

• Answer-choice verification

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Practice 1-2

Choose the best answer. Solutions begin after Question 50.

1. What is 40% of 200?��A. 80 B. 90 C. 75 D. 160 E. 5

2. If 5x+8=48, what is x?��A. 8 B. 7 C. 13 D. 13 E. 9

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Practice 3-4

Choose the best answer. Solutions begin after Question 50.

3. A cyclist travels 60 miles per hour for 2 hours. How many miles does the cyclist travel?��A. 180 B. 122 C. 120 D. 62 E. 60

4. The average of 13, 21, 23 and x is 18. What is x?��A. 19 B. 20 C. 18 D. 15 E. 11

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Practice 5-6

Choose the best answer. Solutions begin after Question 50.

5. What is 12×13−12?��A. 131 B. 149 C. 168 D. 144 E. 156

6. What is 40% of 140?��A. 3 B. 56 C. 100 D. 66 E. 51

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Practice 7-8

Choose the best answer. Solutions begin after Question 50.

7. If 4x+5=17, what is x?��A. 8 B. 3 C. 9 D. 4 E. 2

8. A cyclist travels 35 miles per hour for 3 hours. How many miles does the cyclist travel?��A. 70 B. 108 C. 140 D. 38 E. 105

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Practice 9-10

Choose the best answer. Solutions begin after Question 50.

9. The average of 11, 22, 22 and x is 18. What is x?��A. 18 B. 13 C. 21 D. 17 E. 22

10. What is 17×8−17?��A. 153 B. 124 C. 136 D. 111 E. 119

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Practice 11-12

Choose the best answer. Solutions begin after Question 50.

11. What is 40% of 80?��A. 32 B. 40 C. 2 D. 42 E. 27

12. If 3x+2=26, what is x?��A. 5 B. 9 C. 13 D. 8 E. 7

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Practice 13-14

Choose the best answer. Solutions begin after Question 50.

13. A cyclist travels 60 miles per hour for 4 hours. How many miles does the cyclist travel?��A. 300 B. 180 C. 64 D. 240 E. 244

14. The average of 16, 14, 21 and x is 18. What is x?��A. 21 B. 18 C. 26 D. 17 E. 25

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Practice 15-16

Choose the best answer. Solutions begin after Question 50.

15. What is 22×18−22?��A. 356 B. 374 C. 396 D. 418 E. 379

16. What is 40% of 180?��A. 140 B. 4 C. 67 D. 72 E. 82

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Practice 17-18

Choose the best answer. Solutions begin after Question 50.

17. If 2x+7=13, what is x?��A. 6 B. 4 C. 2 D. 9 E. 3

18. A cyclist travels 35 miles per hour for 5 hours. How many miles does the cyclist travel?��A. 140 B. 180 C. 175 D. 210 E. 40

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Practice 19-20

Choose the best answer. Solutions begin after Question 50.

19. The average of 14, 15, 20 and x is 18. What is x?��A. 18 B. 16 C. 19 D. 23 E. 27

20. What is 27×13−27?��A. 378 B. 351 C. 329 D. 311 E. 324

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Practice 21-22

Choose the best answer. Solutions begin after Question 50.

21. What is 40% of 120?��A. 3 B. 43 C. 80 D. 48 E. 58

22. If 7x+4=60, what is x?��A. 13 B. 11 C. 7 D. 8 E. 9

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Practice 23-24

Choose the best answer. Solutions begin after Question 50.

23. A cyclist travels 60 miles per hour for 2 hours. How many miles does the cyclist travel?��A. 62 B. 60 C. 122 D. 180 E. 120

24. The average of 12, 16, 19 and x is 18. What is x?��A. 15 B. 18 C. 29 D. 21 E. 25

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Practice 25-26

Choose the best answer. Solutions begin after Question 50.

25. What is 14×8−14?��A. 103 B. 98 C. 90 D. 126 E. 112

26. What is 40% of 220?��A. 98 B. 180 C. 5 D. 83 E. 88

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Practice 27-28

Choose the best answer. Solutions begin after Question 50.

27. If 6x+1=19, what is x?��A. 7 B. 4 C. 8 D. 3 E. 2

28. A cyclist travels 35 miles per hour for 3 hours. How many miles does the cyclist travel?��A. 105 B. 140 C. 38 D. 70 E. 108

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Practice 29-30

Choose the best answer. Solutions begin after Question 50.

29. The average of 10, 17, 18 and x is 18. What is x?��A. 18 B. 27 C. 15 D. 31 E. 23

30. What is 19×18−19?��A. 305 B. 323 C. 342 D. 361 E. 328

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Practice 31-32

Choose the best answer. Solutions begin after Question 50.

31. What is 40% of 160?��A. 4 B. 120 C. 64 D. 59 E. 74

32. If 5x+6=46, what is x?��A. 8 B. 7 C. 11 D. 9 E. 13

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Practice 33-34

Choose the best answer. Solutions begin after Question 50.

33. A cyclist travels 60 miles per hour for 4 hours. How many miles does the cyclist travel?��A. 244 B. 240 C. 64 D. 300 E. 180

34. The average of 15, 18, 23 and x is 18. What is x?��A. 21 B. 20 C. 18 D. 12 E. 16

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Practice 35-36

Choose the best answer. Solutions begin after Question 50.

35. What is 24×13−24?��A. 288 B. 336 C. 275 D. 312 E. 293

36. What is 40% of 100?��A. 40 B. 2 C. 50 D. 35 E. 60

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Practice 37-38

Choose the best answer. Solutions begin after Question 50.

37. If 4x+3=15, what is x?��A. 7 B. 8 C. 2 D. 4 E. 3

38. A cyclist travels 35 miles per hour for 5 hours. How many miles does the cyclist travel?��A. 210 B. 175 C. 180 D. 140 E. 40

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Practice 39-40

Choose the best answer. Solutions begin after Question 50.

39. The average of 13, 19, 22 and x is 18. What is x?��A. 22 B. 14 C. 18 D. 23 E. 22

40. What is 29×8−29?��A. 261 B. 232 C. 195 D. 208 E. 203

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Practice 41-42

Choose the best answer. Solutions begin after Question 50.

41. What is 40% of 200?��A. 90 B. 160 C. 5 D. 75 E. 80

42. If 3x+8=32, what is x?��A. 10 B. 8 C. 9 D. 11 E. 7

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Practice 43-44

Choose the best answer. Solutions begin after Question 50.

43. A cyclist travels 60 miles per hour for 2 hours. How many miles does the cyclist travel?��A. 122 B. 180 C. 62 D. 120 E. 60

44. The average of 11, 20, 21 and x is 18. What is x?��A. 17 B. 18 C. 16 D. 20 E. 24

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Practice 45-46

Choose the best answer. Solutions begin after Question 50.

45. What is 16×18−16?��A. 272 B. 288 C. 304 D. 277 E. 254

46. What is 40% of 140?��A. 66 B. 56 C. 3 D. 51 E. 100

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Practice 47-48

Choose the best answer. Solutions begin after Question 50.

47. If 2x+5=11, what is x?��A. 5 B. 7 C. 2 D. 4 E. 3

48. A cyclist travels 35 miles per hour for 3 hours. How many miles does the cyclist travel?��A. 38 B. 105 C. 140 D. 70 E. 108

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Practice 49-50

Choose the best answer. Solutions begin after Question 50.

49. The average of 16, 21, 20 and x is 18. What is x?��A. 19 B. 15 C. 20 D. 18 E. 11

50. What is 21×13−21?��A. 239 B. 252 C. 273 D. 294 E. 257

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Answer Key

Questions 1-50

1. A�2. A�3. C�4. D�5. D�6. B�7. B�8. E�9. D�10. E

11. A�12. D�13. D�14. A�15. B�16. D�17. E�18. C�19. D�20. E

21. D�22. D�23. E�24. E�25. B�26. E�27. D�28. A�29. B�30. B

31. C�32. A�33. B�34. E�35. A�36. A�37. E�38. B�39. C�40. E

41. E�42. B�43. D�44. D�45. A�46. B�47. E�48. B�49. B�50. B

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Solutions 1-2

Check the method, not just the letter.

1. Answer: A. 80��40% of 200 = 40/100 × 200 = 80.

2. Answer: A. 8��Subtract 8, then divide by 5: x=(48−8)/5=8.

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Solutions 3-4

Check the method, not just the letter.

3. Answer: C. 120��Distance = rate × time = 60×2=120.

4. Answer: D. 15��The total must be 4×18=72. Subtract the known sum 57 to get x=15.

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Solutions 5-6

Check the method, not just the letter.

5. Answer: D. 144��Factor 12: 12(13−1)=12×12=144.

6. Answer: B. 56��40% of 140 = 40/100 × 140 = 56.

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Solutions 7-8

Check the method, not just the letter.

7. Answer: B. 3��Subtract 5, then divide by 4: x=(17−5)/4=3.

8. Answer: E. 105��Distance = rate × time = 35×3=105.

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Solutions 9-10

Check the method, not just the letter.

9. Answer: D. 17��The total must be 4×18=72. Subtract the known sum 55 to get x=17.

10. Answer: E. 119��Factor 17: 17(8−1)=17×7=119.

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Solutions 11-12

Check the method, not just the letter.

11. Answer: A. 32��40% of 80 = 40/100 × 80 = 32.

12. Answer: D. 8��Subtract 2, then divide by 3: x=(26−2)/3=8.

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Solutions 13-14

Check the method, not just the letter.

13. Answer: D. 240��Distance = rate × time = 60×4=240.

14. Answer: A. 21��The total must be 4×18=72. Subtract the known sum 51 to get x=21.

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Solutions 15-16

Check the method, not just the letter.

15. Answer: B. 374��Factor 22: 22(18−1)=22×17=374.

16. Answer: D. 72��40% of 180 = 40/100 × 180 = 72.

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Solutions 17-18

Check the method, not just the letter.

17. Answer: E. 3��Subtract 7, then divide by 2: x=(13−7)/2=3.

18. Answer: C. 175��Distance = rate × time = 35×5=175.

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Solutions 19-20

Check the method, not just the letter.

19. Answer: D. 23��The total must be 4×18=72. Subtract the known sum 49 to get x=23.

20. Answer: E. 324��Factor 27: 27(13−1)=27×12=324.

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Solutions 21-22

Check the method, not just the letter.

21. Answer: D. 48��40% of 120 = 40/100 × 120 = 48.

22. Answer: D. 8��Subtract 4, then divide by 7: x=(60−4)/7=8.

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Solutions 23-24

Check the method, not just the letter.

23. Answer: E. 120��Distance = rate × time = 60×2=120.

24. Answer: E. 25��The total must be 4×18=72. Subtract the known sum 47 to get x=25.

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Solutions 25-26

Check the method, not just the letter.

25. Answer: B. 98��Factor 14: 14(8−1)=14×7=98.

26. Answer: E. 88��40% of 220 = 40/100 × 220 = 88.

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Solutions 27-28

Check the method, not just the letter.

27. Answer: D. 3��Subtract 1, then divide by 6: x=(19−1)/6=3.

28. Answer: A. 105��Distance = rate × time = 35×3=105.

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Solutions 29-30

Check the method, not just the letter.

29. Answer: B. 27��The total must be 4×18=72. Subtract the known sum 45 to get x=27.

30. Answer: B. 323��Factor 19: 19(18−1)=19×17=323.

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Solutions 31-32

Check the method, not just the letter.

31. Answer: C. 64��40% of 160 = 40/100 × 160 = 64.

32. Answer: A. 8��Subtract 6, then divide by 5: x=(46−6)/5=8.

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Solutions 33-34

Check the method, not just the letter.

33. Answer: B. 240��Distance = rate × time = 60×4=240.

34. Answer: E. 16��The total must be 4×18=72. Subtract the known sum 56 to get x=16.

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Solutions 35-36

Check the method, not just the letter.

35. Answer: A. 288��Factor 24: 24(13−1)=24×12=288.

36. Answer: A. 40��40% of 100 = 40/100 × 100 = 40.

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Solutions 37-38

Check the method, not just the letter.

37. Answer: E. 3��Subtract 3, then divide by 4: x=(15−3)/4=3.

38. Answer: B. 175��Distance = rate × time = 35×5=175.

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Solutions 39-40

Check the method, not just the letter.

39. Answer: C. 18��The total must be 4×18=72. Subtract the known sum 54 to get x=18.

40. Answer: E. 203��Factor 29: 29(8−1)=29×7=203.

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Solutions 41-42

Check the method, not just the letter.

41. Answer: E. 80��40% of 200 = 40/100 × 200 = 80.

42. Answer: B. 8��Subtract 8, then divide by 3: x=(32−8)/3=8.

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Solutions 43-44

Check the method, not just the letter.

43. Answer: D. 120��Distance = rate × time = 60×2=120.

44. Answer: D. 20��The total must be 4×18=72. Subtract the known sum 52 to get x=20.

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Solutions 45-46

Check the method, not just the letter.

45. Answer: A. 272��Factor 16: 16(18−1)=16×17=272.

46. Answer: B. 56��40% of 140 = 40/100 × 140 = 56.

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Solutions 47-48

Check the method, not just the letter.

47. Answer: E. 3��Subtract 5, then divide by 2: x=(11−5)/2=3.

48. Answer: B. 105��Distance = rate × time = 35×3=105.

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Solutions 49-50

Check the method, not just the letter.

49. Answer: B. 15��The total must be 4×18=72. Subtract the known sum 57 to get x=15.

50. Answer: B. 252��Factor 21: 21(13−1)=21×12=252.