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Another reason to eliminate B is that we do not know how well or not so well private school kids perform on the standardized tests. All we know is that there is a lower teacher-to-children ration in the classrooms. But it does not say anything whether it improves the scores or not.
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I want to explore a hypothetical answer choice that isn't listed:
→ Move to Nesbit County and enroll the child in a private school there.

My reasoning is that this option would combine two positive signals from the passage:
1. Private schools have a higher teacher-to-student ratio (mentioned as the reason Jasper residents prefer them)
2. Nesbit County as a whole seems to have adopted the modern education system (the passage says Nesbit's schools outperform due to this adoption, but doesn't explicitly restrict this to public schools alone)

So the hypothetical option layers both advantages - Nesbit's modern education system AND the higher teacher-to-student ratio of private schools.
Would this hypothetical answer choice be stronger or weaker than E, and why?

Specifically, are we justified in inferring that Nesbit's modern education adoption extends to its private schools, or does the passage restrict that claim strictly to public schools? If the latter, does the higher teacher-to-student ratio alone make this option better or worse than E?
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yashhw thats quite a thought lets look how we can identify.

Responding to your 1st query about Hypothetical choice that " Move to Nesbit County and enroll the child in a private school there" as stronger or weaker in comparison to E.

For this we have to look at the question stem " For the residents of Jasper County whose children go to the county’s public schools, which of the following options would most likely ensure an improved performance of their children in standardized college-entrance exams, only on the basis of the information given in the passage" it specifically mentioned "whose children go to the county’s public schools" So the hypothetical version is neither strengthening nor weaken because it fails to capture county public specificity.

Now to your second query " are we justified in inferring that Nesbit's modern education adoption extends to its private schools, or does the passage restrict that claim strictly to public schools? If the latter, does the higher teacher-to-student ratio alone make this option better or worse than E?"

Now it is not JUSTIFIED, we can't infer that info, we only told about modern education adoption in Nesbit county Public High school, enrollment in private is happening may be because of the frustration from Jasper county or better resources in comparison, or maybe modern education in private schools is adopted before Nasbit but the actual reason is not known, and all these reasons can be a possibility. Inference is something which is 100% justifiable from argument. Also, the question is about county public school, how the teacher student ratio is playing the part in improving the scores we dont know.

Hope this helps
yashhw
I want to explore a hypothetical answer choice that isn't listed:
→ Move to Nesbit County and enroll the child in a private school there.

My reasoning is that this option would combine two positive signals from the passage:
1. Private schools have a higher teacher-to-student ratio (mentioned as the reason Jasper residents prefer them)
2. Nesbit County as a whole seems to have adopted the modern education system (the passage says Nesbit's schools outperform due to this adoption, but doesn't explicitly restrict this to public schools alone)

So the hypothetical option layers both advantages - Nesbit's modern education system AND the higher teacher-to-student ratio of private schools.
Would this hypothetical answer choice be stronger or weaker than E, and why?

Specifically, are we justified in inferring that Nesbit's modern education adoption extends to its private schools, or does the passage restrict that claim strictly to public schools? If the latter, does the higher teacher-to-student ratio alone make this option better or worse than E?
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I like the solution - it’s helpful.
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The question states "which of the following options would most likely ensure an improved performance of their children in standardized college-entrance exams, only on the basis of the information given in the passage".

As per the argument, the reference of improved performance of children in standardized college-entrance exams is mentioned only while talking about comparison with Nesbit County’s public high Schools.

The part two of the argument 'In recent years, more and more Jasper County residents have been enrolling their children in private high schools, where the teacher-to-student ratio is traditionally higher than that in public schools, and enrollment in Jasper County’s public high schools has dwindled as a result' there is no reference mentioned of standardized college-entrance exams, and if we think somehow that private schools because of high teacher-to-student ratio would result in improved performance for college-entrance exam - that will be our assumption and that is something the question explicitly asks us not to use; and answer only on the basis of the information given in the passage.

Hence, we can eliminate all other options and pick E - which states - Move to Nesbit County and enroll their child in that county’s public schools.

That was my thought process while answering this question. Hope that helps.
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