SAT Math Practice Question #709 (Hard (800)) | Test Citadel
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SAT Math Difficulty: Hard (800)

Digital SAT Math Practice Question #709

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At a large corporation, the engineering department has \( 50\% \) more employees than the marketing department, and the sales department has \( 50\% \) fewer employees than the marketing department. The proportion of employees holding a graduate degree is \( 20\% \) in the sales department, \( 30\% \) in the marketing department, and \( k\% \) in the engineering department. If an employee with a graduate degree is chosen at random from these three departments, the probability that they work in the engineering department is \( \frac{3}{5} \). What is the value of \( k \)?
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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 phenomenally tricky conditional probability problem. The best strategy for this kind of SAT question is to assign a concrete "plug-in" number to the base group. Let the number of employees in the Marketing department be 100. The E...

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

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