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# If 0 < a < 1/b <1 then which of the following must be true ?

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Re: If 0 < a < 1/b <1 then which of the following must be true ? [#permalink]
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Given that $$0 < a < \frac{1}{b} <1$$ and we need to find which of the following must be true?

Now, $$0 < a < \frac{1}{b} <1$$ => 0 < a < 1
=> a > $$a^2$$ (Ex: if a = 0.1 then $$a^2$$ = $$0.1^2$$ = 0.01 < 0.1)

$$0 < a < \frac{1}{b} <1$$ => $$0 < \frac{1}{b} <1$$
=> $$\frac{1}{b} <1$$ and b is positive

Multiplying with b on the both the sides we get
b > 1 => b > a
Also, $$b^2$$ > b (Ex: if b = 2 then $$b^2$$ = $$2^2$$ = 4 > 2)

=> $$b^2 > b > a > a^2$$