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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 ?
admin
2014-08-13
32
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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