2025 AMC 8 Problem 7
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In This Page:
To help you master 2025 AMC 8 Problem 7, this page includes:
- The original AMC problem to try, plus the correct answer
- Clear, step-by-step solutions using different methods
- Key ideas, useful formulas, and takeaways you can apply to similar problems
- Related problems from past AMC exams, plus new practice problems that build the same skills
Want more practice? Scroll down to download Think Academy’s AMC 8 practice packs and keep building your AMC 8 skills.
2025 AMC8 Problem 7
7.
On the most recent exam on Prof. Xochi’s class, students earned a score of at least , students earned a score of at least , students earned a score of at least , students earned a score of at least , How many students earned a score of at least and less than ?
Solution
Direct Subtraction Method
The group of students who scored at least 80% includes everyone who scored 80% or higher. If we take this entire group and remove the students who scored 90% or higher, we are left with exactly the students whose scores fall between 80% and 89%.
Step 1: Identify the larger group
According to the problem, 50 students earned a score of at least 80%. This is our starting group. It includes everyone who scored in the 80s, 90s, and up to 100%.
Step 2: Identify the group to remove
We only want the students who scored less than 90%. This means we must remove anyone who scored 90% or higher from our larger group. The problem states there are 13 such students.
Step 3: Calculate the difference
Subtract the number of students who scored at least 90% from the total number of students who scored at least 80%. This calculation removes the high scorers and leaves exactly the students who scored at least 80% but less than 90%.
The result is 37, which matches answer choice D. We can verify this by checking that the extra information (95% and 85% thresholds) is just distractor data; any student scoring at least 90% also scored at least 85%, so our direct subtraction is logically sound.
Interval Breakdown Method
We can find the exact number of students in each specific 5-percent score interval by subtracting the overlapping cumulative counts. Then, we can add the specific intervals that make up our target range.
Step 1: Calculate students scoring between 85% and 89%
There are 27 students who scored at least 85%. From this group, 13 students scored 90% or higher. By subtracting these 13 high scorers, we find the number of students who scored at least 85% but less than 90%.
Step 2: Calculate students scoring between 80% and 84%
There are 50 students who scored at least 80%. However, 27 of them scored 85% or higher. Subtracting these leaves the number of students who scored at least 80% but less than 85%.
Step 3: Combine the target intervals
The target range is ‘at least 80% and less than 90%’. This covers the two adjacent intervals we just calculated. We add the two counts together to get the total number of students in this range.
The total is 37, matching choice D. This step-by-step interval breakdown confirms our direct subtraction method (14 + 23 = 37), ensuring no students were double-counted or missed.
Similar Problems in Real Exams
The following five AMC 8 problems are closely related to AMC 8 2025 Question 7. These real AMC 8 problems test the same key concept—Charts, Distributions & Data Interpretation. Click any problem to learn and practice, then continue to the adapted practice section later in this article for more problems to try.
2022 AMC 8 Problem 15
2020 AMC 8 Problem 14
2018 AMC 8 Problem 8
2017 AMC 8 Problem 2
2011 AMC 8 Problem 11
Adapted Problems to Practice
What Formulas Do You Need for This Problem?
- Set Difference for Subsets:
If every item in Group B is also in Group A, then the number of items in Group A but NOT in Group B is found by subtracting the size of B from the size of A.
Group B must be a subset of Group A (meaning B is fully contained inside A). Anyone who scores at least 90% has automatically scored at least 80%. Therefore, the 'at least 90%' group is a subset of the 'at least 80%' group, allowing us to use direct subtraction.
Key Takeaway: Remember This Strategy for Next Time
A problem gives cumulative totals using phrases like 'at least', 'at most', or 'greater than'.
Try: Subtract the smaller overlapping group from the larger group to find the exact number of items in the boundary between them.
Why: Cumulative totals contain subsets. Removing a smaller subset from a larger set leaves exactly the items that are in the larger set but not in the smaller one.
A problem provides more numbers and categories than seem necessary to answer the question.
Try: Focus only on the specific boundaries you need to define your target group. You do not always have to use every number provided in the problem.
Why: Extra information is often included as a distractor to test whether you truly understand which mathematical conditions define the group you are looking for.
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