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If z=(x+y)/2xy and 0<y<z<1 which of the following

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If z=(x+y)/2xy and 0<y<z<1 which of the following  [#permalink]

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New post Updated on: 04 Apr 2018, 21:51
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A
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If \(z = \frac{(x+y)}{2xy}\) and \(0<y<x<1,\) which of the following must be true about range of z?

A. \(z<0.5\)
B. \(z>0.5\)
C. \(z\geq{1}\)
D. \(z<1\)
E. \(z>1\)

Originally posted by Jamil1992Mehedi on 04 Apr 2018, 20:50.
Last edited by chetan2u on 04 Apr 2018, 21:51, edited 1 time in total.
updated the question
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Re: If z=(x+y)/2xy and 0<y<z<1 which of the following  [#permalink]

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New post 04 Apr 2018, 21:42
It is already given z < 1 how can option E be correct ?
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Re: If z=(x+y)/2xy and 0<y<z<1 which of the following  [#permalink]

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New post 04 Apr 2018, 21:49
teaserbae wrote:
It is already given z < 1 how can option E be correct ?


Question seems to be wrong..since nothing is given for x..

what if x=0.Then it will be undefined..

Might be x<1 instead of Z
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If z=(x+y)/2xy and 0<y<z<1 which of the following  [#permalink]

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New post 04 Apr 2018, 21:50
Jamil1992Mehedi wrote:
If \(z = \frac{(x+y)}{2xy}\) and \(0<y<z<1,\) which of the following must be true?

A. \(z<0.5\)
B. \(z>0.5\)
C. \(z\geq{1}\)
D. \(z<1\)
E. \(z>1\)



the choices give away answer..
z<0.5 is a part of z<1, so cannot be the answer...
z>1 or \(z\geq{1}\) is a part of z>0.5, so cannot be the answer...
Actually answer should be B or D...

But here it seems the question wants to know for what range of z does it hold true
also it will be \(0<y<x<1\) and not \(0<y<z<1,\)

so lets find the answer..
\(z = \frac{(x+y)}{2xy}\)...
now since x and y are both <1, their ADDITION will always be MORE than their PRODUCT*2, so \(x+y>2xy..........\frac{x+y}{2xy}>1\)..... z>1
E
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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If z=(x+y)/2xy and 0<y<z<1 which of the following &nbs [#permalink] 04 Apr 2018, 21:50
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If z=(x+y)/2xy and 0<y<z<1 which of the following

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