# 2021 AMC 12B Problems/Problem 12

Revision as of 20:26, 11 February 2021 by Soysoy4444 (talk | contribs) (Created page with "Let <math>x</math> be the greatest integer, <math>y</math> be the smallest, <math>z</math> be the sum of the numbers in S excluding <math>x</math> and <math>y</math>, and <mat...")

Let be the greatest integer, be the smallest, be the sum of the numbers in S excluding and , and be the number of elements in S.

Then,

Firstly, when the greatest integer is removed,

When the smallest integer is also removed,

When the greatest integer is added back,

We are given that

After you substitute , you have 3 equations with 3 unknowns , and .

This can be easily solved to yield , , .

average value of all integers in the set , D)

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