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

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

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New post 15 Jul 2018, 08:56
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A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

87% (01:14) correct 13% (01:29) wrong based on 36 sessions

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

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New post 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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New post 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.

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