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If 0 < a < 1/b<1 then which of the following must be true ? (A) a>b>

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If 0 < a < 1/b<1 then which of the following must be true ? (A) a>b> [#permalink]

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New post 07 Jun 2017, 18:34
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E

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75% (01:15) correct 25% (01:33) wrong based on 135 sessions

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

(A) a > b > b^2
(B) b > a > a^2 > b^2
(C) b^2 > a > a^2 > b
(D) b^2 > a^2 > b > a
(E) b^2 > b > a > a^2

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Re: If 0 < a < 1/b<1 then which of the following must be true ? (A) a>b> [#permalink]

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New post 07 Jun 2017, 18:50
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hazelnut wrote:
If 0 < a < 1/b <1 then which of the following must be true ?

(A) a > b > b^2
(B) b > a > a^2 > b^2
(C) b^2 > a > a^2 > b
(D) b^2 > a^2 > b > a
(E) b^2 > b > a > a^2


\(0<a<1 \implies 0 < a^2 < a < 1\)

\(0 < \frac{1}{b} < 1 \implies b > 1 \implies b^2 > b > 1\)

Hence \(b^2 > b > 1 > a > a^2 > 0\)

The correct answer is E
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Re: If 0 < a < 1/b<1 then which of the following must be true ? (A) a>b> [#permalink]

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New post 01 Aug 2017, 17:21
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1
Representing on the number line we have something like this:
Attachment:
numberline.png
numberline.png [ 1.05 KiB | Viewed 908 times ]


Now picking numbers, e.g: a=0.1 and b=5, so that 1/b=0.2

The only valid option is E, as 25>5>0.1>0.01
Re: If 0 < a < 1/b<1 then which of the following must be true ? (A) a>b>   [#permalink] 01 Aug 2017, 17:21
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