4/19/10

Test 7 Section 7 - #16 (page 788)

It's a lot easier to think about this question if you put it in an xy-coordinate plane.  Let's make Diane's house the origin:
What we want to do is compare the green dotted line to the distance Diane usually drives, and see how much shorter her drive would be if she could just go directly.  Easy part first: her usual commute is 16 mi + 15 mi + 4 mi = 35 mi.  How do we know how long the green line is?  Well, it looks suspiciously like a right triangle to me, so let's Pythagorize it!  (Note: don't say "Pythagorize" in public...people will look at you funny.)  We'll call our green line d:

152 + 202  = d2
225 + 400 = d2
625 = d2
25 = d
As is very often the case on the SAT, since they prefer to work with integers, we're looking at a big ol' 3-4-5 triangle (15-20-25 in this case).  Get quick at recognizing those, and you'll save yourself a few seconds by avoiding the Pythagorean Theorem.

OK. So Diane usually drives 35 miles, but if she could drive directly, it would only be 25 miles.  Her drive would be 10 miles shorter.  That's choice (C).

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