SAT Math Practice Question #499 (Hard (800)) | Test Citadel
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SAT Math Difficulty: Hard (800)

Digital SAT Math Practice Question #499

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A marketing survey categorizes respondents by age ("Under 30" or "30 & Older") and by their preferred subscription tier ("Basic" or "Premium"). The following relationships are true: - The number of respondents "Under 30" who prefer "Basic" is \( p \). - The number of respondents "Under 30" who prefer "Premium" is \( p + 50 \). - The number of respondents "30 & Older" who prefer "Basic" is \( 3p \). - The number of respondents "30 & Older" who prefer "Premium" is \( 2p - 10 \). The total number of respondents in the survey is \( 600 \). If a respondent is selected at random from those who prefer the "Premium" tier, what is the probability that the respondent is "Under 30"?
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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 question tests conditional probability embedded within an algebraic two-way table. It requires strict attention to the wording of the final condition. Step 1: Set up the total population equation to solve for \( p \). We know the sum o...

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

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