2012 AMC 12A Problem 1

Below is the professionally curated solution for Problem 1 of the 2012 AMC 12A, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2012 AMC 12A solutions, or check the answer key.

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Concepts:absolute value

Difficulty rating: 770

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:

The bug crawls $|-6-(-2)| = 4$ units on the first leg and $|5-(-6)| = 11$ units on the second leg.

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

Thus, the correct answer is E.

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