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  3. Compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given,

Compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given,

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问题 Compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given, and select one of the following four answer choices:
(A)Quantity A is greater.
(B)Quantity B is greater.
(C)The two quantities are equal.
(D)The relationship cannot be determined from the information given.
A symbol that appears more than once in a question has the same meaning throughout the question.
选项
答案D
解析 The figure looks like a right triangle with legs of length 5 + y and 12 - y and hypotenuse of length 13. If y = 0, then the sides of the triangle have lengths 5, 12, and 13. This triangle is in fact a right triangle because 52 + 122 = 132. So the angle labeled x° is a right angle; that is, x = 90. In this case, Quantity A is equal to Quantity B.
Now consider another value of y, say y=1, to see if the triangle is still a right triangle in this case. If y = 1, then the sides of the triangle have lengths 6, 11, and 13. This triangle is not a right triangle because 62 + 112≠132. So the angle labeled x° is not a right angle; that is, x≠90. In this case, Quantity A is not equal to Quantity B.
Because Quantity A is equal to Quantity B in one case and Quantity A is not equal to Quantity B in another case, the correct answer is Choice D.
This explanation uses the following strategies.
Strategy 10: Trial and Error
Strategy 13: Determine Whether a Conclusion Follows from the Information Given
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