SAT Math Practice Question #788 (Hard (800)) | Test Citadel
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SAT Math Difficulty: Hard (800)

Digital SAT Math Practice Question #788

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

A radioactive isotope decays such that its mass decreases by \( p\\% \) every \( h \) hours. If the mass of the isotope decreases by \( q\\% \) every \( 3h \) hours, which of the following equations correctly expresses \( q \) in terms of \( p \)?
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Socratic AI Engine Step-by-Step Derivation
0ms Precomputed
Tactical Insight (Hint 1)

Express the growth/decay rate in factor form: \( A = P(1 \pm r)^t \). Beware whether \( t \) is in years, months, or quarters.

Elimination Framework (Hint 2)

Desmos Tactical Shortcut: Plot the left-hand side and right-hand side as separate equations (e.g. \( y_1 = f(x) \) and \( y_2 = g(x) \)). Click the intersection points directly to read exact coordinates.

Masterclass Solution & Distractor Trap Analysis

The SAT tests your ability to translate percentage decreases into algebraic multipliers and compound them over time. Step 1: Define the multiplier for a percentage decrease. If a quantity decreases by \( p\\% \), its remaining amount is fou...

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

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