In the figure above, a path from point A to point D is determined by moving upward or to the right along the grid lines. How many different paths can be drawn from A to D that do not include either B or C ?
Level of Difficulty E
This is an easy problem as long as you are systematic in your approach, which is a useful tip on many SAT questions. Start on the path that moves along the upper left-most path, carefully working your way toward the path that moves along the lower right-most path. Counting paths that do not involve corners B or C, you will find there are four, which is choice B.
If you would like to see some examples of more sophisticated graph theory problems (well beyond the SAT level), go to advanced graph theory. Don't panic - you won't be solving problems like these until you get to college.
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