SAT Math Practice Question #729 (Hard (800)) | Test Citadel
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SAT Math Difficulty: Hard (800)

Digital SAT Math Practice Question #729

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

In a certain school district, the average (arithmetic mean) test score for High School A is \( 84 \), and the average test score for High School B is \( 72 \). High School A has \( m \) students and High School B has \( n \) students. If the district opens a new High School C by randomly transferring exactly \( 20\% \) of the students from High School A and \( 30\% \) of the students from High School B to School C, what is the expected average test score of the students at High School C in terms of \( m \) and \( n \)? (Assume the transferred students had average scores perfectly identical to their original school's overall averages).
Select Your Answer:
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

This question rigorously tests your conceptual understanding of weighted averages using abstract algebraic variables. Let's break it down logically. The formula for an average is: \( \text{Average} = \frac{\text{Total Sum of Scores}}{\text{...

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

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