MathDB
Obligatory Statistics Problem

Source: 2022 AMC 10B P10 / 2022 AMC 12B P7

November 17, 2022
AMCAMC 10statistics2022 AMC2022 AMC 10B2022 AMC 12BAMC 12

Problem Statement

Camila writes down five positive integers. The unique mode of these integers is 22 greater than their median, and the median is 22 greater than their arithmetic mean. What is the least possible value for the mode?
<spanclass=latexbold>(A)</span>5<spanclass=latexbold>(B)</span>7<spanclass=latexbold>(C)</span>9<spanclass=latexbold>(D)</span>11<spanclass=latexbold>(E)</span>13<span class='latex-bold'>(A) </span>5\qquad<span class='latex-bold'>(B) </span>7\qquad<span class='latex-bold'>(C) </span>9\qquad<span class='latex-bold'>(D) </span>11\qquad<span class='latex-bold'>(E) </span>13