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01 Apr 2012, 03:47
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D
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Difficulty:
95%
(hard)
Question Stats:
42% (02:13) correct
58%
(02:19)
wrong
based on 699
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
(1) \(\frac{1}{w} +\frac{1}{x} +\frac{1}{y} +\frac{1}{z} = 1\).
(2) \(\frac{1}{w} > \frac{1}{4}\).
from gmatquantproblems
01 Apr 2012, 04:06
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BN1989
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.
Answer: D.
01 Aug 2014, 16:43
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BN1989
(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
D is the answer
