SAT Math Practice Question #670 (Hard (800)) | Test Citadel
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SAT Math Difficulty: Hard (800)

Digital SAT Math Practice Question #670

Test your problem-solving accuracy on this official-caliber item. Select an answer choice to check your reasoning instantly.

In a certain school district, all high schools are classified as either Category A or Category B. The Category A schools have an average of \( 400 \) students per school, while the Category B schools have an average of \( 900 \) students per school. If exactly \( 60\% \) of the high school students in the entire district attend a Category A school, what fraction of the high schools in the district are Category A schools?
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Socratic AI Engine Step-by-Step Derivation
0ms Precomputed
Tactical Insight (Hint 1)

Break down the given equation or algebraic constraints step-by-step. Isolate the target variable before substituting known quantities.

Elimination Framework (Hint 2)

Elimination Shortcut: Check the extremes or test answer choices starting with C to binary search the correct magnitude.

Masterclass Solution & Distractor Trap Analysis

Prepare for a masterclass in weighted averages! This is an elite-tier SAT problem because it tempts you to confuse the percentage of *students* with the percentage of *schools*. Let's define our variables clearly: Let \( A \) be the number ...

Distractor Analysis: Trap choice eliminates careless test-takers who confuse roots with coordinates...

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