Solution

Note that all of the choices are possible orderings of the quantities \(\frac{1}{a}\) , \(\frac{1}{b}\) 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 \(\frac{1}{a}\) must be greater than 1. Since b is greater than 1, the value of \(\frac{1}{b}\) must be less than 1. So you know that \(\frac{1}{a} > 1\) and that \(\frac{1}{b} < 1\) or combined in one expression \(\frac{1}{b} < 1 < \frac{1}{a}\).

The answer is \(D\)

You can also assume values
if 0<a<1<b
so a = 0.5
b = 2
now take reciprocals
1/a = 1/0.5 = 2
1/b = 1/2 = 0.5
Arrangement would be
0.5<1<2
=1/b<1<1/a

Option D matches
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Concept: Taking a reciprocal of an inequality reverses it.
So since a < 1 < b, then the reciprocal would be 1/a > 1 > 1/b.
The answer matching this is D.

Best way to do this is to take reciprocal, as taking reciprocal, inequality sign reverse. Hence, option is D.
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