SAT Math Practice Question #408 (Hard (800)) | Test Citadel
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SAT Math Difficulty: Hard (800)

Digital SAT Math Practice Question #408

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A company operates entirely out of a North office and a South office. Currently, the average (arithmetic mean) salary of employees in the North office is \( \$80,000 \), the average salary in the South office is \( \$60,000 \), and the overall average salary for all employees company-wide is \( \$72,000 \). The company plans to hire 10 new employees for the North office at an average salary of \( \$90,000 \) and 20 new employees for the South office at an average salary of \( \$50,000 \). If these hires are made, the new overall average salary for the entire company will be \( \$70,000 \). What was the original total number of employees in the company before the new hires?
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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

This is a highly rigorous statistics problem testing your mastery of weighted averages and systems of equations. Let's do this step-by-step. Let \( N \) be the original number of employees in the North office, and \( S \) be the original nu...

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

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