Achievable logoAchievable logo
AMC
Sign in
Sign up
Purchase
Textbook
Practice exams
Support
How it works
Exam catalog
Mountain with a flag at the peak
Textbook
Introduction
1. Algebra
2. Geometry
3. Number theory
4. Counting and probability
5. Intermediate topics (AMC 10/12)
6. Advanced topics (AMC 12)
7. General approaches
8. Practical strategies
8.1 Backsolve
8.2 Estimate
8.3 Eliminate
Wrapping up
Achievable logoAchievable logo
8.3 Eliminate
Achievable AMC
8. Practical strategies

Eliminate

4 min read
Font
Discuss
Share
Feedback

This chapter applies to all AMC 8/10/12 test takers.

The elimination method is different from the estimation method.

  • Estimation: You make a reasonable estimate, then choose between 2 or 3 answer choices that are close to that estimate.
  • Elimination: You rule out answer choices that must be wrong based on clear logic - number properties, minimums/maximums, units, or other constraints.

Elimination isn’t meant to replace full solution methods. It’s most useful when you’re short on time and need to make a well-supported guess.

Here are a few examples where you can eliminate answer choices for different reasons.

Example: The question below is from 2018 AMC 8

The clock in Sri’s car, which is not accurate, gains time at a constant rate. One day as he begins shopping, he notes that his car clock and his watch (which is accurate) both say 12:00 noon. When he is done shopping, his watch says 12:30 and his car clock says 12:35. Later that day, Sri loses his watch. He looks at his car clock and it says 7:00. What is the actual time?
A. 5:50
B. 6:00
C. 6:30
D. 6:55
E. 8:10

(spoiler)

Answer: B. 6:00 You can eliminate answer choices for quick, definite reasons.

  • Eliminate E: 8:10 is later than 7:00, but the car clock is known to gain time (run fast). That means the actual time must be earlier than what the car clock shows, so E can’t be correct.
  • Eliminate D: The car clock reads exactly 7:00 (minutes end in 0). With a constant gain rate, the relationship between actual minutes and car-clock minutes is consistent, so the actual minutes can’t end in 5 at the moment the car clock’s minutes end in 0.

With a bit more calculation, you’ll find the correct answer is B.

Example: The question below is from 2021 AMC 10A

A cart rolls down a hill, travelling 5 inches the first second and accelerating so that during each successive 1-second time interval, it travels 7 inches more than during the previous 1-second interval. The cart takes 30 seconds to reach the bottom of the hill. How far, in inches, does it travel?
A. 215
B. 360
C. 2992
D. 3195
E. 3242

(spoiler)

Answer: D. 3195 You can quickly eliminate A and B by looking at the distance traveled in the last second.

  • The distances form an arithmetic sequence: 5,12,19,…
  • The 30th-second distance is 5+29⋅7=208.

So in the final second alone, the cart travels 208 inches. That means the total over 30 seconds must be much larger than 215 or 360, so A and B are impossible.

Example: The question below is from 2017 AMC 10B

Points A(11,9) and B(2,−3) are vertices of △ABC with AB=AC. The altitude from A meets the opposite side at D(−1,3). What are the coordinates of point C?
A. (−8,9)
B. (−4,8)
C. (−4,9)
D. (−2,3)
E. (−1,0)

(spoiler)

Answer: C. (−4,9) A quick sketch (or even just comparing coordinates) helps you eliminate choices.

Since D(−1,3) lies on BC and is the foot of the altitude from A, point C must lie on the line through D that forms side BC. From the diagram you’d expect, C should be to the left of D (smaller x) and above D (larger y).

  • Choices D and E have y≤3, so they can’t be above D.

That eliminates D and E immediately. A full solution then leads to C.

Common themes

  • Answer choices that are far in proximity to the cluster (outliers) are unlikely to be correct in the AMC questions.
  • Eliminating answer choices is also useful when using the backsolving method. As a result, you will likely have to plug in fewer answer choices to find the correct answer.
  • If you know that the correct answer must be, even, odd, positive, negative, an integer, fraction, square, cube or fraction, you can eliminate any answer choices that do not fit the desired characteristic.
  • For AMC 10/12, do not guess if you have not eliminated 2 or more answer choices. It is more beneficial to keep the 1.5 points by leaving the answer blank than gambling for 6 points and choosing between 4 or all 5 options. For AMC 8, there is no benefit to leaving an answer blank.

Elimination method overview\

  • Distinct from estimation; uses logic to rule out impossible answers
  • Relies on number properties, constraints, or answer format
  • Best for time pressure or narrowing choices, not as a replacement for full solutions

Example 1: Car clock problem\

  • Eliminate answers inconsistent with problem facts (e.g., time must be earlier if clock runs fast)
  • Use properties like minute alignment to rule out answers (e.g., minutes digit mismatch)

Example 2: Cart on hill (arithmetic sequence)\

  • Identify arithmetic sequence in problem setup
  • Eliminate answers too small based on maximum term or sum estimation

Example 3: Triangle coordinates\

  • Use geometric reasoning (position relative to a point or line)
  • Eliminate answers with impossible coordinate values (e.g., y-coordinate not above reference point)

Common elimination strategies\

  • Outlier answers (far from cluster) are rarely correct
  • Use elimination to reduce backsolving workload
  • Eliminate choices based on required properties:
    • Even/odd, positive/negative, integer/fraction, square/cube, etc.
  • AMC 10/12: Only guess if at least 2 choices are eliminated; otherwise, leave blank
  • AMC 8: No penalty for guessing, so always answer

Sign up for free to take 6 quiz questions on this topic

Previous
Next  | Wrapping up
All rights reserved ©2016 - 2026 Achievable, Inc.

Eliminate

This chapter applies to all AMC 8/10/12 test takers.

The elimination method is different from the estimation method.

  • Estimation: You make a reasonable estimate, then choose between 2 or 3 answer choices that are close to that estimate.
  • Elimination: You rule out answer choices that must be wrong based on clear logic - number properties, minimums/maximums, units, or other constraints.

Elimination isn’t meant to replace full solution methods. It’s most useful when you’re short on time and need to make a well-supported guess.

Here are a few examples where you can eliminate answer choices for different reasons.

Example: The question below is from 2018 AMC 8

The clock in Sri’s car, which is not accurate, gains time at a constant rate. One day as he begins shopping, he notes that his car clock and his watch (which is accurate) both say 12:00 noon. When he is done shopping, his watch says 12:30 and his car clock says 12:35. Later that day, Sri loses his watch. He looks at his car clock and it says 7:00. What is the actual time?
A. 5:50
B. 6:00
C. 6:30
D. 6:55
E. 8:10

(spoiler)

Answer: B. 6:00 You can eliminate answer choices for quick, definite reasons.

  • Eliminate E: 8:10 is later than 7:00, but the car clock is known to gain time (run fast). That means the actual time must be earlier than what the car clock shows, so E can’t be correct.
  • Eliminate D: The car clock reads exactly 7:00 (minutes end in 0). With a constant gain rate, the relationship between actual minutes and car-clock minutes is consistent, so the actual minutes can’t end in 5 at the moment the car clock’s minutes end in 0.

With a bit more calculation, you’ll find the correct answer is B.

Example: The question below is from 2021 AMC 10A

A cart rolls down a hill, travelling 5 inches the first second and accelerating so that during each successive 1-second time interval, it travels 7 inches more than during the previous 1-second interval. The cart takes 30 seconds to reach the bottom of the hill. How far, in inches, does it travel?
A. 215
B. 360
C. 2992
D. 3195
E. 3242

(spoiler)

Answer: D. 3195 You can quickly eliminate A and B by looking at the distance traveled in the last second.

  • The distances form an arithmetic sequence: 5,12,19,…
  • The 30th-second distance is 5+29⋅7=208.

So in the final second alone, the cart travels 208 inches. That means the total over 30 seconds must be much larger than 215 or 360, so A and B are impossible.

Example: The question below is from 2017 AMC 10B

Points A(11,9) and B(2,−3) are vertices of △ABC with AB=AC. The altitude from A meets the opposite side at D(−1,3). What are the coordinates of point C?
A. (−8,9)
B. (−4,8)
C. (−4,9)
D. (−2,3)
E. (−1,0)

(spoiler)

Answer: C. (−4,9) A quick sketch (or even just comparing coordinates) helps you eliminate choices.

Since D(−1,3) lies on BC and is the foot of the altitude from A, point C must lie on the line through D that forms side BC. From the diagram you’d expect, C should be to the left of D (smaller x) and above D (larger y).

  • Choices D and E have y≤3, so they can’t be above D.

That eliminates D and E immediately. A full solution then leads to C.

Common themes

  • Answer choices that are far in proximity to the cluster (outliers) are unlikely to be correct in the AMC questions.
  • Eliminating answer choices is also useful when using the backsolving method. As a result, you will likely have to plug in fewer answer choices to find the correct answer.
  • If you know that the correct answer must be, even, odd, positive, negative, an integer, fraction, square, cube or fraction, you can eliminate any answer choices that do not fit the desired characteristic.
  • For AMC 10/12, do not guess if you have not eliminated 2 or more answer choices. It is more beneficial to keep the 1.5 points by leaving the answer blank than gambling for 6 points and choosing between 4 or all 5 options. For AMC 8, there is no benefit to leaving an answer blank.
Key points

Elimination method overview\

  • Distinct from estimation; uses logic to rule out impossible answers
  • Relies on number properties, constraints, or answer format
  • Best for time pressure or narrowing choices, not as a replacement for full solutions

Example 1: Car clock problem\

  • Eliminate answers inconsistent with problem facts (e.g., time must be earlier if clock runs fast)
  • Use properties like minute alignment to rule out answers (e.g., minutes digit mismatch)

Example 2: Cart on hill (arithmetic sequence)\

  • Identify arithmetic sequence in problem setup
  • Eliminate answers too small based on maximum term or sum estimation

Example 3: Triangle coordinates\

  • Use geometric reasoning (position relative to a point or line)
  • Eliminate answers with impossible coordinate values (e.g., y-coordinate not above reference point)

Common elimination strategies\

  • Outlier answers (far from cluster) are rarely correct
  • Use elimination to reduce backsolving workload
  • Eliminate choices based on required properties:
    • Even/odd, positive/negative, integer/fraction, square/cube, etc.
  • AMC 10/12: Only guess if at least 2 choices are eliminated; otherwise, leave blank
  • AMC 8: No penalty for guessing, so always answer

More from Practical strategies

  • Backsolve
  • Estimate