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fraction problem, seriously driving me bananas!

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by killer1387 » Mon Mar 05, 2012 12:04 am
M GETTING W/Z=(W/X)^3.
whats d answer or options?
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by dhiren8182 » Mon Mar 05, 2012 12:18 am
Que:w/x=x/y=y/z
w/x=x/y
so w=x^2/y
x/y=y/z
so z=y^2/x
therefore w/z=x^3/y^3
w/x=x^2.x/y.y^2
so w/x=w.x^2/z
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by Mr.Hollywood » Mon Mar 05, 2012 12:25 am
killer1387 wrote:M GETTING W/Z=(W/X)^3.
whats d answer or options?
That is actually the answer I was given, would you mind sharing your steps?
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by hritupon » Mon Mar 05, 2012 1:24 am
w/x=x/y
=>y=x^2/w .......(1)

and

x/y=y/z
=>z=y^2/x........(2)

Now

w/z
=w(x/y^2) (using z from 2)
=(w/y)*(x/y)
=(w/y)*(w/x) (because w/x=x/y)
=w^2/(xy)
=(w^2/x)*(1/y)
=(w^2/x)*(w/x^2) (using y from 1)
=(w/x)^3
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by Mr.Hollywood » Mon Mar 05, 2012 2:12 am
hritupon wrote:w/x=x/y
=>y=x^2/w .......(1)

and

x/y=y/z
=>z=y^2/x........(2)

Now

w/z
=w(x/y^2) (using z from 2)
=(w/y)*(x/y)
=(w/y)*(w/x) (because w/x=x/y)
=w^2/(xy)
=(w^2/x)*(1/y)
=(w^2/x)*(w/x^2) (using y from 1)
=(w/x)^3
My god this is brilliant! Who'd thought of that?! I noticed you started out with y and z, any particular reason why you did that? I started with w and x but apparently went no where. Another question is how do you approach this kind of questions? Thank you so very much!
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by GMATGuruNY » Mon Mar 05, 2012 4:07 am
Mr.Hollywood wrote:w/x=x/y=y/z Question is, represent w/z with w and x
Since the GMAT would provide answer choices, we could plug in values that satisfy the equation:

w/x = x/y = y/z
2/4 = 4/8 = 8/16
w/z = 2/16 = 1/8. This would be our target.

The next step would be to plug w=2 and x=4 into the answers to which yields our target of 1/8.

(w/x)³ = (2/4)³ = (1/2)³ = 1/8.
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by killer1387 » Mon Mar 05, 2012 7:43 am
repeat..
Last edited by killer1387 on Mon Mar 05, 2012 7:47 am, edited 1 time in total.
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by killer1387 » Mon Mar 05, 2012 7:44 am
Mr.Hollywood wrote:
killer1387 wrote:M GETTING W/Z=(W/X)^3.
whats d answer or options?
That is actually the answer I was given, would you mind sharing your steps?
w/x=x/y=y/z=k (say)
w=kx-----------------(1)
z=y/k=x/(k^2)--------(2)
w/z=k^3 (from 1 & 2)

put k=w/x as given in question
hence w/z=(w/x)^3
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by killer1387 » Mon Mar 05, 2012 7:45 am
...repeat post....
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