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

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Manager
Joined: 12 Oct 2011
Posts: 117
GMAT 1: 700 Q48 V37
GMAT 2: 720 Q48 V40
If w > x > y > z > 0, is z < 4?  [#permalink]

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01 Apr 2012, 03:47
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22
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Difficulty:

95% (hard)

Question Stats:

44% (01:33) correct 56% (01:43) wrong based on 720 sessions

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

(1) $$\frac{1}{w} +\frac{1}{x} +\frac{1}{y} +\frac{1}{z} = 1$$.

(2) $$\frac{1}{w} > \frac{1}{4}$$.

from gmatquantproblems
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If w > x > y > z > 0, is z < 4?  [#permalink]

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01 Apr 2012, 04:06
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BN1989 wrote:

from gmatquantproblems

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) $$\frac{1}{w} +\frac{1}{x} +\frac{1}{y} +\frac{1}{z} = 1$$. 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) $$\frac{1}{w} > \frac{1}{4}$$. 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]

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01 Aug 2014, 16:43
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BN1989 wrote:
If w>x>y>z>0, is z<4?

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

(2) 1/w > 1/4.

from gmatquantproblems

(1) since w>x>y>z>0, 1/w<1/x< 1/y<1/z
so 1/w +1/x +1/y +1/z < 1/z + 1/z + 1/z + 1/z = 4/z
so 4/z > 1, we have z<4

(2) w>z so, 1/z> 1/w> 1/4, so z<4

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Re: If w > x > y > z > 0, is z < 4?  [#permalink]

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27 Jun 2018, 23:37
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Re: If w > x > y > z > 0, is z < 4? &nbs [#permalink] 27 Jun 2018, 23:37
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