SAT Math Practice Question #450 (Hard (800)) | Test Citadel
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SAT Math Difficulty: Hard (800)

Digital SAT Math Practice Question #450

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

A dataset consists of 99 positive integers \( a_1, a_2, \ldots, a_{99} \) such that \( a_1 \le a_2 \le \ldots \le a_{99} \). The median of the dataset is 50, the mean is 60, and the range is 120. What is the maximum possible value of \( a_{99} \)?
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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)

Desmos Tactical Shortcut: Type the function directly into Desmos. Tap the peak or trough of the curve to instantly reveal the extrema coordinates \( (h, k) \).

Masterclass Solution & Distractor Trap Analysis

This is a masterpiece of a Statistics logic puzzle. To maximize the largest value (\( a_{99} \)), we have to balance the rigid constraints of the median, mean, range, and ordering. Let's map out our constraints: 1. 99 positive integers, sor...

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

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