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If w > x > y > z > 0, is z < 4?
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20 Mar 2011, 13:14
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36% (00:18) correct 64% (01:59) wrong based on 14 sessions
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If w > x > y > z > 0, is z \frac{1}{4}[/m]. OPEN DISCUSSION OF THIS QUESTION IS HERE: ifwxyz0isz129991.html== Message from the GMAT Club Team == THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION. This discussion does not meet community quality standards. It has been retired. If you would like to discuss this question please repost it in the respective forum. Thank you! To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative  Verbal Please note  we may remove posts that do not follow our posting guidelines. Thank you.
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Re: If w > x > y > z > 0, is z < 4?
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20 Mar 2011, 13:25
(1) We could transform the initial condition: 0<1/W<1/X<1/Y<1/Z If Z>4, then 1/Z<1/4 and three other number 1/W, 1/Y, 1/X are also less than 1/4, so their sum could not be equal to 1. So (1) is sufficient to say that Z<4. So, the answer is A (2) alone does not say us anything about Z
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Re: If w > x > y > z > 0, is z < 4?
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20 Mar 2011, 17:12
Given 0 < Z < y<X <w
1. sufficient if z >4 => 1/z <0.25 , then the given sum will never be 1. Hence this is enough to say z cannot be greater than 4.
2. sufficient
w<4 =>z<w<4 => z<4, enough to answer the question.
Answer is D.



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Re: If w > x > y > z > 0, is z < 4?
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20 Mar 2011, 18:05
@Spidy001, I've a query here : if z >4 => 1/z <0.25 , then the given sum will never be 1. Hence this is enough to say z cannot be greater than 4. How is the above true ? If z > 4 => z < 0.25 then z can have max value(s) as 0.24, 0.249 etc or lesser values as 0.05 etc. and the values of y, x and w can be more than this and hence the total may be 1, right ? (2) is clearly sufficient as we have > W, and w > z so clearly z < 4. Not sure if I'm doing anything wrong in the analysis of (1), someone please enlighten me. Regards, Subhash
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Re: If w > x > y > z > 0, is z < 4?
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20 Mar 2011, 18:23
No. As W>X>Y>Z 1/W < 1/X < 1/Y < 1/Z Also as 1/Z < 1/4 , => 1/W < 1/X < 1/Y < 1/Z < 1/4 so with this condition their sum will never be equal to 1. Hope its clear now. subhashghosh wrote: @Spidy001, I've a query here :
if z >4 => 1/z <0.25 , then the given sum will never be 1. Hence this is enough to say z cannot be greater than 4.
How is the above true ? If z > 4 => z < 0.25 then z can have max value(s) as 0.24, 0.249 etc or lesser values as 0.05 etc. and the values of y, x and w can be more than this and hence the total may be 1, right ?
(2) is clearly sufficient as we have > W, and w > z so clearly z < 4.
Not sure if I'm doing anything wrong in the analysis of (1), someone please enlighten me.
Regards, Subhash



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Re: If w > x > y > z > 0, is z < 4?
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20 Mar 2011, 19:10
OA is D.
for 1) as Spidy said, if z >= 4 then, 1/z =< 0.25 and since w,x, and y are greater than z, 1/w, 1/x, 1/y and 1/z will all be less than 0.25 and their sum will never amount to 1. 4*(# less than .25)<1 Thus z has to be less than 4.



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Re: If w > x > y > z > 0, is z < 4?
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20 Mar 2011, 21:21
Yes, I had mistaken this bit : As W>X>Y>Z 1/W < 1/X < 1/Y < 1/Z Thanks for your reply. Kudos
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Re: If w > x > y > z > 0, is z < 4?
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20 Mar 2011, 21:58
if W>X>Y>Z>0, for positive integers 1/W<1/X<1/Y<1/Z
1. 1/W + 1/X + 1/Y + 1/Z = 1 To check whether Z > 4 or not, lets put Z = 5 this means 1/W + 1/X + 1/Y = 11/5= 4/5 or 0.8. average value of each term would be 0.266. But 1/z = 0.2. We know from question stem that 1/Z > 1/X , 1/Y, 1/Z. Thus we know z is not greater than 4. Hence 1 is sufficient to answer this question
2. 1/W >1/4 this implies that 1/Z >1/4. or Z<4. This also correctly answers the question.
Since both statements are sufficient by themselves, D



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Re: If w > x > y > z > 0, is z < 4?
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12 Dec 2017, 21:42
Given W>X>Y>Z>0
Asked Z>4?
Stat#1: 1/W +1/X +1/Y +1/Z = 1 and W>X>Y>Z>0 can only possible if w,x,y,z are fractions so suff.
Stat#2: 1/W > 1/4 => w>4 { as w>0 } so suff.
D



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Re: If w > x > y > z > 0, is z < 4?
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12 Dec 2017, 21:56
If w > x > y > z > 0, is z \frac{1}{y}>\frac{1}{x}>\frac{1}{w}[/m] 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 [b]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. OPEN DISCUSSION OF THIS QUESTION IS HERE: ifwxyz0isz129991.html== Message from the GMAT Club Team == THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION. This discussion does not meet community quality standards. It has been retired. If you would like to discuss this question please repost it in the respective forum. Thank you! To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative  Verbal Please note  we may remove posts that do not follow our posting guidelines. Thank you.
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Re: If w > x > y > z > 0, is z < 4? &nbs
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