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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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Senior SC Moderator
Joined: 14 Nov 2016
Posts: 1283
Location: Malaysia
If 0 < a < 1/b<1 then which of the following must be true ? (A) a>b> [#permalink]

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07 Jun 2017, 18:34
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Difficulty:

25% (medium)

Question Stats:

73% (01:13) correct 27% (01:33) wrong based on 127 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

[Reveal] Spoiler: OA

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Senior CR Moderator
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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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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 $$b^2 > b > 1 > a > a^2 > 0$$

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Joined: 13 Apr 2017
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Concentration: General Management, Economics
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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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01 Aug 2017, 17:21
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Representing on the number line we have something like this:
Attachment:

numberline.png [ 1.05 KiB | Viewed 716 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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