School Administrator: The number of fourteen year olds in Britain who are considered "gifted" that is who score higher than 90% of their peers on the mandatory secondary school entrance exam (MSEEE) - has increased steadily over the past decade.
If the school administrator's findings are correct, which of the following can be concluded on the basis of those findings?
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In logical reasoning questions, focus on what can be directly concluded from the given information. Avoid making assumptions or choosing options that are merely possible explanations. The link between a fixed percentage and a changing absolute number is a common pattern.
There has been at least some improvement in British education over the past decade.
The number of British fourteen year olds who are not considered gifted has decreased over the past decade.
The number of British fourteen year olds taking the MSEEE has increased over the past decade.
Preparation for the MSEEE has improved in British schools over the past decade.
The percentage of British fourteen year olds who are considered gifted has increased as a percentage of the total population.
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The Correct Option isC
Solution and Explanation
Step 1: Understanding the Question:
The core of the question lies in the definition of "gifted." A student is "gifted" if they score higher than 90% of their peers. This means they are in the top 10% of all students who take the exam. The administrator states that the absolute number of these gifted students has increased. We need to find the most logical conclusion from this fact. Step 2: Detailed Explanation:
Let \(N_{total}\) be the total number of students taking the MSEEE.
Let \(N_{gifted}\) be the number of students considered "gifted".
By definition, the "gifted" students are the top 10% of those who take the exam.
Therefore, the percentage of gifted students among test-takers is fixed at 10%.
So, we can write the relationship:
\[ N_{gifted} = 10% \times N_{total} = 0.10 \times N_{total} \]
The problem states that \(N_{gifted}\) has increased over the past decade.
Since \(N_{gifted}\) is directly proportional to \(N_{total}\) (with the constant of proportionality being 0.10), if \(N_{gifted}\) increases, then \(N_{total}\) must also increase.
Let's evaluate the options based on this deduction:
(A) and (D): Improvement in education or preparation might be a reason for higher scores overall, but the "gifted" category is relative (top 10%). An overall improvement wouldn't change the percentage. Thus, this cannot be concluded for certain.
(B): If \(N_{total}\) has increased, the number of non-gifted students (which is 90% of \(N_{total}\)) would also have increased. This option states the opposite.
(C): This aligns perfectly with our deduction. If the number of students in the top 10% has gone up, the total number of students taking the exam must have gone up.
(E): The percentage of gifted students \textit{among test-takers} is constant at 10%. The statement doesn't provide enough information to make a conclusion about the total population of all fourteen-year-olds in Britain (including those who don't take the exam).
Step 3: Final Answer:
The only conclusion that logically follows from the administrator's findings is that the total number of students taking the Mandatory Secondary School Entrance Exam (MSEEE) has increased.
