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# If a = 0.729, which of the following must be true?

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Math Expert
Joined: 02 Sep 2009
Posts: 53061
If a = 0.729, which of the following must be true?  [#permalink]

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22 Jan 2019, 00:27
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Difficulty:

25% (medium)

Question Stats:

78% (00:54) correct 22% (01:33) wrong based on 62 sessions

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If a = 0.729, which of the following must be true?

A $$a > a^2 > √a$$

B $$a > √a > a^2$$

C $$a^2 > a > √a$$

D $$√a > a^2 > a$$

E $$√a > a > a^2$$

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Re: If a = 0.729, which of the following must be true?  [#permalink]

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22 Jan 2019, 00:30
1
Bunuel wrote:
If a = 0.729, which of the following must be true?

A $$a > a^2 > √a$$

B $$a > √a > a^2$$

C $$a^2 > a > √a$$

D $$√a > a^2 > a$$

E $$√a > a > a^2$$

a = 0.729.

pure fraction .

if we square a fraction we will get even smaller fraction . Square root will enlarge the fraction.

Manager
Joined: 14 Nov 2017
Posts: 60
Re: If a = 0.729, which of the following must be true?  [#permalink]

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22 Jan 2019, 00:36
E
You can simplify this using a=1/2

a=1/2
a^2=1/4
(a)^-2>a if 1>a>0

So

(a)^-2>a>a^2

These rules are valid for every number in the 1>x>0 range
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Re: If a = 0.729, which of the following must be true?  [#permalink]

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22 Jan 2019, 03:57
Bunuel wrote:
If a = 0.729, which of the following must be true?

A $$a > a^2 > √a$$

B $$a > √a > a^2$$

C $$a^2 > a > √a$$

D $$√a > a^2 > a$$

E $$√a > a > a^2$$

sqrt 0.729 >a>a^2
IMO E
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Re: If a = 0.729, which of the following must be true?   [#permalink] 22 Jan 2019, 03:57
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