To determine the lowest mark that qualifies for a scholarship awarded to the top 10% of students at school Y, we need to follow a systematic approach. Here’s how we can break it down step-by-step: Step 1: Understand the Problem The school is awarding scholarships to the top 10% of students based on their marks. This means we need to find out what the lowest mark is that falls within this top 10%. Step 2: Gather Information To solve this problem, we need to know: - The total number of students in the school. - The distribution of marks among these students. However, since we do not have the exact number of students or their marks, we will analyze the options provided to determine which mark corresponds to the top 10%. Step 3: Analyze the Options The options given are: - A. 86% - B. 82% - C. 78% - D. 74% Step 4: Determine the Top 10% To find the lowest mark for the top 10%, we can assume a hypothetical number of students. Let’s say there are 100 students in total (this makes calculations easier).

• Top 10% of 100 students = 10 students.

This means we need to find the mark that is the lowest among the top 10 students. Step 5: Evaluate the Options Now, we will evaluate the options based on the assumption that the marks are distributed in a way that allows us to identify the lowest mark for the top 10%.

1. Option A: 86%
2. If 86% is the lowest mark for the top 10%, then all students in the top 10% must have marks of 86% or higher. This would mean that at least 10 students scored 86% or more.
3. Option B: 82%
4. If 82% is the lowest mark for the top 10%, then at least 10 students scored 82% or higher. This could be possible, but it would mean that there are students scoring between 74% and 82% who are not in the top 10%.
5. Option C: 78%
6. If 78% is the lowest mark for the top 10%, then at least 10 students scored 78% or higher. This suggests that there could be many students scoring below 78%, which is plausible.
7. Option D: 74%
8. If 74% is the lowest mark for the top 10%, then at least 10 students scored 74% or higher. This is unlikely because it would mean that a significant number of students scored below 74%, which would not typically represent the top 10%.

Step 6: Conclusion Given the analysis, Option C (78%) is the most reasonable choice for the lowest mark that qualifies for a scholarship. It allows for a distribution where the top 10% can be clearly defined without having too many students below the threshold. Why Other Options Are Incorrect

• Option A (86%): This is too high to be the lowest mark for the top 10% unless the majority of students scored significantly lower, which is less likely.
• Option B (82%): While this could be a possibility, it does not account for a wider distribution of scores that would allow for a more inclusive top 10%.
• Option D (74%): This is too low to represent the top 10%, as it would imply that many students scored below this mark, which is not typical for a top percentile.

Revision Summary

• To find the lowest mark for the top 10%, consider the total number of students and their score distribution.
• Analyze each option based on the assumption of a reasonable score distribution.
• The lowest mark for the top 10% should be a score that allows for a clear distinction between the top students and the rest.
• In this case, 78% is the most logical choice for the lowest qualifying mark for a scholarship.