Chapter 32

This chapter gives you the answers and explanations for the Mathematical Reasoning practice test in Chapter 31. The first question you may ask yourself is why you should bother with the explanations if you got the answers right. The simple answer is: The explanation walks you through the problem, from the question to the correct answer. If you made an error in the question and got it wrong, the explanation can save you from a lot of frustration. By following the steps, you can discover why and where you went wrong and figure out a way to not repeat the error on similar questions on the real test.

**B. 20 miles.**This problem is a test of your knowledge of how to use the Pythagorean theorem. Sketch out a map for this problem: Due south and due west are at right angles. So Yvonne’s journey is a triangle, with the last part being the hypotenuse. Pythagoras (the guy who, as you may expect, came up with the Pythagorean theorem) said that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides (*a*^{2}+*b*^{2}=*c*^{2}). Thus, the square of the last leg of Yvonne’s journey equals 472 + 172 = 2,498. The square root of 2,498 is 49.98. Because none of the numbers in this problem has any numbers beyond the decimal point, you can round the answer to 50. However, the question asks how much further Yvonne must travel: She ended up traveling 17 + 50 = 67 miles and would ...

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