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AMC 8 Challenge Lab

Lesson 1: Number Sense & Arithmetic Strategies

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

Number Sense & Arithmetic Strategies

• 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 19×21−19?��A. 418 B. 399 C. 380 D. 359 E. 385

2. What is 30% of 80?��A. 24 B. 2 C. 34 D. 50 E. 19

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Practice 3-4

Choose the best answer. Solutions begin after Question 50.

3. What is the greatest common factor of 30 and 56?��A. 840 B. 4 C. 1 D. 8 E. 2

4. If 6x+3=21, what is x?��A. 2 B. 8 C. 4 D. 9 E. 3

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Practice 5-6

Choose the best answer. Solutions begin after Question 50.

5. The arithmetic sequence starts 3, 10, 17, ... . What is the 11th term?��A. 78 B. 77 C. 66 D. 80 E. 73

6. What is 24×16−24?��A. 384 B. 365 C. 408 D. 360 E. 344

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Practice 7-8

Choose the best answer. Solutions begin after Question 50.

7. What is 30% of 180?��A. 6 B. 150 C. 64 D. 54 E. 49

8. What is the greatest common factor of 18 and 56?��A. 504 B. 1 C. 2 D. 8 E. 4

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Practice 9-10

Choose the best answer. Solutions begin after Question 50.

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

10. The arithmetic sequence starts 3, 9, 15, ... . What is the 8th term?��A. 50 B. 45 C. 48 D. 51 E. 39

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Practice 11-12

Choose the best answer. Solutions begin after Question 50.

11. What is 29×11−29?��A. 290 B. 319 C. 295 D. 279 E. 348

12. What is 30% of 120?��A. 46 B. 36 C. 90 D. 4 E. 31

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Practice 13-14

Choose the best answer. Solutions begin after Question 50.

13. What is the greatest common factor of 48 and 56?��A. 4 B. 14 C. 16 D. 8 E. 336

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

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Practice 15-16

Choose the best answer. Solutions begin after Question 50.

15. The arithmetic sequence starts 3, 8, 13, ... . What is the 13th term?��A. 63 B. 68 C. 68 D. 65 E. 58

16. What is 16×21−16?��A. 325 B. 299 C. 352 D. 320 E. 336

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Practice 17-18

Choose the best answer. Solutions begin after Question 50.

17. What is 30% of 220?��A. 190 B. 76 C. 66 D. 7 E. 61

18. What is the greatest common factor of 36 and 56?��A. 2 B. 10 C. 4 D. 8 E. 504

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Practice 19-20

Choose the best answer. Solutions begin after Question 50.

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

20. The arithmetic sequence starts 3, 7, 11, ... . What is the 10th term?��A. 40 B. 44 C. 39 D. 35 E. 43

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Practice 21-22

Choose the best answer. Solutions begin after Question 50.

21. What is 21×16−21?��A. 320 B. 357 C. 315 D. 336 E. 299

22. What is 30% of 160?��A. 5 B. 130 C. 58 D. 48 E. 43

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Practice 23-24

Choose the best answer. Solutions begin after Question 50.

23. What is the greatest common factor of 24 and 56?��A. 168 B. 14 C. 8 D. 4 E. 16

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

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Practice 25-26

Choose the best answer. Solutions begin after Question 50.

25. The arithmetic sequence starts 3, 6, 9, ... . What is the 15th term?��A. 48 B. 49 C. 42 D. 45 E. 50

26. What is 26×11−26?��A. 249 B. 312 C. 265 D. 286 E. 260

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Practice 27-28

Choose the best answer. Solutions begin after Question 50.

27. What is 30% of 100?��A. 40 B. 25 C. 70 D. 30 E. 3

28. What is the greatest common factor of 54 and 56?��A. 1512 B. 4 C. 1 D. 2 E. 8

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Practice 29-30

Choose the best answer. Solutions begin after Question 50.

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

30. The arithmetic sequence starts 3, 5, 7, ... . What is the 12th term?��A. 30 B. 24 C. 27 D. 25 E. 23

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Practice 31-32

Choose the best answer. Solutions begin after Question 50.

31. What is 13×21−13?��A. 239 B. 265 C. 260 D. 273 E. 286

32. What is 30% of 200?��A. 55 B. 6 C. 170 D. 60 E. 70

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Practice 33-34

Choose the best answer. Solutions begin after Question 50.

33. What is the greatest common factor of 42 and 56?��A. 14 B. 7 C. 168 D. 28 E. 20

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

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Practice 35-36

Choose the best answer. Solutions begin after Question 50.

35. The arithmetic sequence starts 3, 10, 17, ... . What is the 9th term?��A. 52 B. 66 C. 63 D. 64 E. 59

36. What is 18×16−18?��A. 270 B. 288 C. 254 D. 306 E. 275

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Practice 37-38

Choose the best answer. Solutions begin after Question 50.

37. What is 30% of 140?��A. 110 B. 4 C. 37 D. 52 E. 42

38. What is the greatest common factor of 30 and 56?��A. 2 B. 1 C. 4 D. 8 E. 840

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Practice 39-40

Choose the best answer. Solutions begin after Question 50.

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

40. The arithmetic sequence starts 3, 9, 15, ... . What is the 14th term?��A. 84 B. 86 C. 87 D. 81 E. 75

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Practice 41-42

Choose the best answer. Solutions begin after Question 50.

41. What is 23×11−23?��A. 235 B. 219 C. 230 D. 253 E. 276

42. What is 30% of 80?��A. 34 B. 2 C. 19 D. 24 E. 50

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Practice 43-44

Choose the best answer. Solutions begin after Question 50.

43. What is the greatest common factor of 18 and 56?��A. 504 B. 4 C. 2 D. 1 E. 8

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

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Practice 45-46

Choose the best answer. Solutions begin after Question 50.

45. The arithmetic sequence starts 3, 8, 13, ... . What is the 11th term?��A. 48 B. 58 C. 53 D. 58 E. 55

46. What is 28×21−28?��A. 539 B. 588 C. 565 D. 560 E. 616

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Practice 47-48

Choose the best answer. Solutions begin after Question 50.

47. What is 30% of 180?��A. 54 B. 150 C. 6 D. 64 E. 49

48. What is the greatest common factor of 48 and 56?��A. 336 B. 16 C. 14 D. 8 E. 4

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Practice 49-50

Choose the best answer. Solutions begin after Question 50.

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

50. The arithmetic sequence starts 3, 7, 11, ... . What is the 8th term?��A. 27 B. 32 C. 31 D. 36 E. 35

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Answer Key

Questions 1-50

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

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

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

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

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

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Solutions 1-2

Check the method, not just the letter.

1. Answer: C. 380��Factor 19: 19(21−1)=19×20=380.

2. Answer: A. 24��30% of 80 = 30/100 × 80 = 24.

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Solutions 3-4

Check the method, not just the letter.

3. Answer: E. 2��Prime-factor or Euclidean-algorithm work gives gcd(30,56)=2.

4. Answer: E. 3��Subtract 3, then divide by 6: x=(21−3)/6=3.

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Solutions 5-6

Check the method, not just the letter.

5. Answer: E. 73��a_n=a_1+(n−1)d=3+(11−1)(7)=73.

6. Answer: D. 360��Factor 24: 24(16−1)=24×15=360.

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Solutions 7-8

Check the method, not just the letter.

7. Answer: D. 54��30% of 180 = 30/100 × 180 = 54.

8. Answer: C. 2��Prime-factor or Euclidean-algorithm work gives gcd(18,56)=2.

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Solutions 9-10

Check the method, not just the letter.

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

10. Answer: B. 45��a_n=a_1+(n−1)d=3+(8−1)(6)=45.

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Solutions 11-12

Check the method, not just the letter.

11. Answer: A. 290��Factor 29: 29(11−1)=29×10=290.

12. Answer: B. 36��30% of 120 = 30/100 × 120 = 36.

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Solutions 13-14

Check the method, not just the letter.

13. Answer: D. 8��Prime-factor or Euclidean-algorithm work gives gcd(48,56)=8.

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

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Solutions 15-16

Check the method, not just the letter.

15. Answer: A. 63��a_n=a_1+(n−1)d=3+(13−1)(5)=63.

16. Answer: D. 320��Factor 16: 16(21−1)=16×20=320.

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Solutions 17-18

Check the method, not just the letter.

17. Answer: C. 66��30% of 220 = 30/100 × 220 = 66.

18. Answer: C. 4��Prime-factor or Euclidean-algorithm work gives gcd(36,56)=4.

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Solutions 19-20

Check the method, not just the letter.

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

20. Answer: C. 39��a_n=a_1+(n−1)d=3+(10−1)(4)=39.

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Solutions 21-22

Check the method, not just the letter.

21. Answer: C. 315��Factor 21: 21(16−1)=21×15=315.

22. Answer: D. 48��30% of 160 = 30/100 × 160 = 48.

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Solutions 23-24

Check the method, not just the letter.

23. Answer: C. 8��Prime-factor or Euclidean-algorithm work gives gcd(24,56)=8.

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

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Solutions 25-26

Check the method, not just the letter.

25. Answer: D. 45��a_n=a_1+(n−1)d=3+(15−1)(3)=45.

26. Answer: E. 260��Factor 26: 26(11−1)=26×10=260.

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Solutions 27-28

Check the method, not just the letter.

27. Answer: D. 30��30% of 100 = 30/100 × 100 = 30.

28. Answer: D. 2��Prime-factor or Euclidean-algorithm work gives gcd(54,56)=2.

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Solutions 29-30

Check the method, not just the letter.

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

30. Answer: D. 25��a_n=a_1+(n−1)d=3+(12−1)(2)=25.

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Solutions 31-32

Check the method, not just the letter.

31. Answer: C. 260��Factor 13: 13(21−1)=13×20=260.

32. Answer: D. 60��30% of 200 = 30/100 × 200 = 60.

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Solutions 33-34

Check the method, not just the letter.

33. Answer: A. 14��Prime-factor or Euclidean-algorithm work gives gcd(42,56)=14.

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

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Solutions 35-36

Check the method, not just the letter.

35. Answer: E. 59��a_n=a_1+(n−1)d=3+(9−1)(7)=59.

36. Answer: A. 270��Factor 18: 18(16−1)=18×15=270.

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Solutions 37-38

Check the method, not just the letter.

37. Answer: E. 42��30% of 140 = 30/100 × 140 = 42.

38. Answer: A. 2��Prime-factor or Euclidean-algorithm work gives gcd(30,56)=2.

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Solutions 39-40

Check the method, not just the letter.

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

40. Answer: D. 81��a_n=a_1+(n−1)d=3+(14−1)(6)=81.

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Solutions 41-42

Check the method, not just the letter.

41. Answer: C. 230��Factor 23: 23(11−1)=23×10=230.

42. Answer: D. 24��30% of 80 = 30/100 × 80 = 24.

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Solutions 43-44

Check the method, not just the letter.

43. Answer: C. 2��Prime-factor or Euclidean-algorithm work gives gcd(18,56)=2.

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

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Solutions 45-46

Check the method, not just the letter.

45. Answer: C. 53��a_n=a_1+(n−1)d=3+(11−1)(5)=53.

46. Answer: D. 560��Factor 28: 28(21−1)=28×20=560.

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Solutions 47-48

Check the method, not just the letter.

47. Answer: A. 54��30% of 180 = 30/100 × 180 = 54.

48. Answer: D. 8��Prime-factor or Euclidean-algorithm work gives gcd(48,56)=8.

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Solutions 49-50

Check the method, not just the letter.

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

50. Answer: C. 31��a_n=a_1+(n−1)d=3+(8−1)(4)=31.