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# If 0 < a < 1 < b which of the following is true about the reciprocals

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Math Expert
Joined: 02 Sep 2009
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If 0 < a < 1 < b which of the following is true about the reciprocals  [#permalink]

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15 Jul 2018, 08:56
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If $$0<a<1<b$$ which of the following is true about the reciprocals of a and b ?

A) $$1< \frac{1}{a}< \frac{1}{b}$$

B) $$\frac{1}{a} < 1 < \frac{1}{b}$$

C) $$\frac{1}{a}< \frac{1}{b} < 1$$

D) $$\frac{1}{b} < 1 < \frac{1}{a}$$

E) $$\frac{1}{b}< \frac{1}{a} < 1$$

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If 0 < a < 1 < b which of the following is true about the reciprocals  [#permalink]

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15 Jul 2018, 09:00
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Bunuel wrote:
If $$0<a<1<b$$ which of the following is true about the reciprocals of a and b ?

A) $$1< \frac{1}{a}< \frac{1}{b}$$

B) $$\frac{1}{a} < 1 < \frac{1}{b}$$

C) $$\frac{1}{a}< \frac{1}{b} < 1$$

D) $$\frac{1}{b} < 1 < \frac{1}{a}$$

E) $$\frac{1}{b}< \frac{1}{a} < 1$$

$$a$$ & $$b$$ are positive, so we can cross-multiply without changing the sign of the inequality

$$a<1=>1<\frac{1}{a}$$

and $$1<b=>\frac{1}{b}<1$$, combining both the inequality we will get

$$\frac{1}{b}<1<\frac{1}{a}$$

Option D
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If 0 < a < 1 < b which of the following is true about the reciprocals  [#permalink]

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15 Jul 2018, 10:57
Bunuel wrote:
If $$0<a<1<b$$ which of the following is true about the reciprocals of a and b ?

A) $$1< \frac{1}{a}< \frac{1}{b}$$

B) $$\frac{1}{a} < 1 < \frac{1}{b}$$

C) $$\frac{1}{a}< \frac{1}{b} < 1$$

D) $$\frac{1}{b} < 1 < \frac{1}{a}$$

E) $$\frac{1}{b}< \frac{1}{a} < 1$$

Note : a is a fraction . So, its reciprocal will always be greater than the reciprocal of an integer or proper fraction.

Thus , the reciprocal of a will be greater than 1 and the reciprocal of b will be less than 1.

Option D meets our expectation.

If 0 < a < 1 < b which of the following is true about the reciprocals   [#permalink] 15 Jul 2018, 10:57
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