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# If x, y and z are positive, is x = y/z^2

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If x, y and z are positive, is x = y/z^2 [#permalink]  08 Feb 2013, 13:26
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If x, y and z are positive, is x = y/z^2 ?

(1) $$z= \frac{y}{xz}$$

(2) $$z = \sqrt{\frac{y}{x}}$$
[Reveal] Spoiler: OA

Last edited by Bunuel on 09 Feb 2013, 01:16, edited 2 times in total.
Edited the question and OA.
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Re: If x, y and z are positive, is x = y/z^2 [#permalink]  08 Feb 2013, 23:40
The correct answer should be D IMO.
If x, y and z are positive, is x = y/z^2 ?

(1) z= y/xz --> Cross multiplying makes it x=y/z^2

(2) z = (y/x)^-2 --> Squaring both sides --> Z^2 = Y/X --> Cross Multiply --> X=Y/Z^2
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Re: If x, y and z are positive, is x = y/z^2 [#permalink]  09 Feb 2013, 01:20
Expert's post
If x, y and z are positive, is x = y/z^2 ?

(1) $$z= \frac{y}{xz}$$ --> multiply by x/z: $$x=\frac{y}{z^2}$$. Sufficient.

(2) $$z = \sqrt{\frac{y}{x}}$$ --> square the expression: $$z^2=\frac{y}{x}$$ --> $$x=\frac{y}{z^2}$$. Sufficient.

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Re: If x, y and z are positive, is x = y/z^2 [#permalink]  19 Jul 2013, 00:36
Question:

If we quickly conclude that the question "is x = y/z^2" can be answered only if we can isolate x on one side and y and z on the other side, would that not be enough to conclude whether or not "x = y/z^2"?

This would save a lot of time, instead of doing calculations you simply determine what you need quickly.

But just to double check with you experts if my reasoning is correct, would this SAME reasoning apply if we were given the info in one of the two statments that: "z = x/y" or for that matter "zy*x = y/z" . These two statments CAN be "solved" with my reasoning because both statments only have x, y and z and thus x can be expressed in terms of y and z. Therefore, we can conclude if "x = y/z^2"
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Re: If x, y and z are positive, is x = y/z^2 [#permalink]  19 Jul 2013, 00:43
Expert's post
aeglorre wrote:
Question:

If we quickly conclude that the question "is x = y/z^2" can be answered only if we can isolate x on one side and y and z on the other side, would that not be enough to conclude whether or not "x = y/z^2"?

This would save a lot of time, instead of doing calculations you simply determine what you need quickly.

But just to double check with you experts if my reasoning is correct, would this SAME reasoning apply if we were given the info in one of the two statments that: "z = x/y" or for that matter "zy*x = y/z" . These two statments CAN be "solved" with my reasoning because both statments only have x, y and z and thus x can be expressed in terms of y and z.

Not sure I understand completely what you mean but if one of the statements were z = x/y, then it wouldn't be sufficient.
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Re: If x, y and z are positive, is x = y/z^2 [#permalink]  19 Jul 2013, 00:52
Bunuel wrote:
aeglorre wrote:
Question:

If we quickly conclude that the question "is x = y/z^2" can be answered only if we can isolate x on one side and y and z on the other side, would that not be enough to conclude whether or not "x = y/z^2"?

This would save a lot of time, instead of doing calculations you simply determine what you need quickly.

But just to double check with you experts if my reasoning is correct, would this SAME reasoning apply if we were given the info in one of the two statments that: "z = x/y" or for that matter "zy*x = y/z" . These two statments CAN be "solved" with my reasoning because both statments only have x, y and z and thus x can be expressed in terms of y and z.

Not sure I understand completely what you mean but if one of the statements were z = x/y, then it wouldn't be sufficient.

What I mean is that if our stem asks us "is x = y/z^2", then what we need in order to determin IF "x = y/z^2" is what x is, in relation to y and z.

Statment 1 gives us an equation where we CAN put x in relation to y and z, thus this equation is enough to determine "is x = y/z^2".
Statment 2 also give us enough for us to put x in relation to y and z, thus we have enough info to determine if "is x = y/z^2"

This is a very quick way in this DS question to conclude whether we have enough info or not, but Im not sure if it is completely bulletproof.

EDIT: Ah.. I see it isn't completely bulleproof because z^2 has two answers, z can be positive or negative, which we don't know, so the statment can be insufficent..
Re: If x, y and z are positive, is x = y/z^2   [#permalink] 19 Jul 2013, 00:52
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