SAT Math Practice Question #350 (Hard (800)) | Test Citadel
TC
Test Citadel
SAT Math Difficulty: Hard (800)

Digital SAT Math Practice Question #350

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

A data set consists of 15 distinct positive integers. The median of the data set is 40, and the range of the data set is 74. What is the maximum possible value of the mean of this data set?
Select Your Answer:
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 an extraordinary statistics problem that requires deep logical optimization. To maximize the mean of a data set, you must maximize the sum of all the elements in that set. Let's build this set strategically. Let the 15 distinct posi...

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

🔒 Citadel Pro Scholar Vault

Unlock Full Solution & 2,600+ Official Drills

Access detailed Socratic steps, trap breakdowns, authentic timed module simulations, and Desmos speed hacks for just $9.99/mo.

Socratic Assistant

Targeted hints without disclosing final solutions.

I am your Socratic tutor. Click one of the quick guidance buttons above or ask a specific question below about a formula or method.