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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.
x>0 and x≠1.
选项
答案D
解析 The two quantities can be simplified as follows.
Quantity A:
Quantity B:
So comparing Quantity A with Quantity B is the same as comparing.
Since you are given that x> 0 and x ≠ 1, and the quantities to be compared involve fractions and exponents, it is reasonable to consider two cases: 0 < x < 1 and x > 1.
Case 1: 02 < x. Therefore , and Quantity A is greater than Quantity B.
Case 2: x>1. If x is a number that satisfies x>1, then x2>x. Therefore, and Quantity B is greater than Quantity A.
In one case Quantity A is greater, and in the other case Quantity B is greater. Thus the correct answer is Choice D.
This explanation uses the following strategies.
Strategy 5: Simplify an Arithmetic or Algebraic Representation
Strategy 8: Search for a Mathematical Relationship
Strategy 11: Divide into Cases
Strategy 13: Determine Whether a Conclusion Follows from the Information Given
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本试题收录于： GRE QUANTITATIVE题库GRE分类
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