MathDB
Impossible Sums

Source: 2015 AMC 10A #20

February 4, 2015
geometryrectangleperimeter

Problem Statement

A rectangle has area A cm2A \text{ cm}^2 and perimeter P cmP \text{ cm}, where AA and PP are positive integers. Which of the following numbers cannot equal A+PA+P?
<spanclass=′latex−bold′>(A)</span>100<spanclass=′latex−bold′>(B)</span>102<spanclass=′latex−bold′>(C)</span>104<spanclass=′latex−bold′>(D)</span>106<spanclass=′latex−bold′>(E)</span>108 <span class='latex-bold'>(A) </span>100\qquad<span class='latex-bold'>(B) </span>102\qquad<span class='latex-bold'>(C) </span>104\qquad<span class='latex-bold'>(D) </span>106\qquad<span class='latex-bold'>(E) </span>108
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