SAT Math Practice Question #600 (Hard (800)) | Test Citadel
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SAT Math Difficulty: Hard (800)

Digital SAT Math Practice Question #600

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

A dataset consists of 100 positive integers. The mean of the dataset is 54, and the median is 60. The sum of the 25 largest integers in the dataset is exactly 2,400. What is the maximum possible value of the largest integer in this dataset?
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Socratic AI Engine Step-by-Step Derivation
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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 an elite descriptive statistics problem testing the concept of maximization under strict constraints. Let's arrange our 100 positive integers in ascending order: \( x_1 \le x_2 \le \dots \le x_{100} \). Goal: Maximize \( x_{100} \)....

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

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