2006 AMC 8 Problem 10

Below is the professionally curated solution for Problem 10 of the 2006 AMC 8, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2006 AMC 8 solutions, or check the answer key.

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Concepts:factor coordinate geometry

Difficulty rating: 1120

10.

Jorge's teacher asks him to plot all the ordered pairs $(w, l)$ of positive integers for which $w$ is the width and $l$ is the length of a rectangle with area $12.$ What should his graph look like?

Solution:

The positive integer factor pairs $(w,l)$ with $wl=12$ are $(1,12),(2,6),(3,4),(4,3),(6,2),$ and $(12,1)$ .

These points form a decreasing set of six points, and only graph A matches them.

Thus, A is the correct answer.

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