2012 AMC 10A Problem 3

Below is the professionally curated solution for Problem 3 of the 2012 AMC 10A, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2012 AMC 10A solutions, or check the answer key.

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Concepts:absolute value

Difficulty rating: 560

A bug crawls along a number line, starting at $-2.$ It crawls to $-6,$ then turns around and crawls to $5.$ How many units does the bug crawl altogether?

$9$

$11$

$13$

$14$

$15$

Solution:

It crawls a distance of $|-2 - (-6)| = |-4| = 4$ when it moves from $-2$ to $-6.$ It then travels a distance of $|-6 - 5| = |-11| = 11$ as it moves from $-6$ to $5.$

The total distance is then $4 + 11 = 15.$

Thus, E is the correct answer.

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