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  3. If 0 < a < 1 < b, which of the following is true about the reciprocals of a and b ?

If 0 < a < 1 < b, which of the following is true about the reciprocals of a and b ?

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问题 If 0 < a < 1 < b, which of the following is true about the reciprocals of a and b ?
选项 A、 
B、 
C、 
D、 
E、 
答案D
解析 To answer this question, you must first look at the answer choices. Note that all of the choices are possible orderings of the quantities 1/a, 1/b, and 1 from least to greatest. So to answer the question, you must put the three quantities in order from least to greatest. The inequality 0 < a < 1 < b tells you that 0 < a < 1 and that b>1. Since a is a value between 0 and 1, the value of 1/a must be greater than 1. Since b is greater than 1, the value of 1/b must be less than 1. So you know that 1/a> 1 and that 1/b < 1, or combined in one expression, 1/b< 1 <1/a, and the correct answer is Choice D.
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