2012 AMC 10A Problem 3

Attempt Problem 3 of the 2012 AMC 10A below, then check your answer against the professionally curated solution 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.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

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

Add the distance from

-2

-6

and from

-6

5

Distance on a number line uses absolute differences

It crawls a distance of

|-2 - (-6)| = |4| = 4

when it moves from

-2

-6.

It then travels a distance of

|-6 - 5| = |-11| = 11

as it moves from

-6

5.

The total distance is then

4 + 11 = 15.

Thus, E is the correct answer.

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