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# If w>x>y>z>0, is z>4?

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If w>x>y>z>0, is z>4? [#permalink]  01 Apr 2012, 03:47
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27% (01:58) correct 72% (01:43) wrong based on 47 sessions
If w>x>y>z>0, is z<4?

(1) 1/w +1/x +1/y +1/z = 1.

(2) 1/w > 1/4.

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Re: If w>x>y>z>0 is z<4? [#permalink]  01 Apr 2012, 04:06
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BN1989 wrote:

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If w>x>y>z>0, is z<4?

We can rewrite given inequality as: \frac{1}{z}>\frac{1}{y}>\frac{1}{x}>\frac{1}{w} and the question becomes whether \frac{1}{z}>\frac{1}{4}?

(1) 1/w +1/x +1/y +1/z = 1. Now, if \frac{1}{z}\leq{\frac{1}{4}} then all other three fractions will also be less than \frac{1}{4} and their sum (the sum of four numbers each of which is less than 1/4) can not add up to 1, hence \frac{1}{z}>\frac{1}{4}. Sufficient.

(2) 1/w > 1/4. Since \frac{1}{z}>\frac{1}{w} then \frac{1}{z} is also more than \frac{1}{4}. Sufficient.

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Re: If w>x>y>z>0, is z>4? [#permalink]  28 May 2013, 05:29
Bumping for review and further discussion.
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Re: If w>x>y>z>0, is z>4?   [#permalink] 28 May 2013, 05:29
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