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If 2xy + z = 9, what is the value of the positive integer z?

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If 2xy + z = 9, what is the value of the positive integer z? [#permalink]  19 Aug 2013, 08:36
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If 2xy + z = 9, what is the value of the positive integer z?

(1) xyz - z^2 = 0

(2) x + y - 3z = -5
[Reveal] Spoiler: OA

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Re: If 2xy + z = 9, what is the value of the positive integer z? [#permalink]  19 Aug 2013, 08:43
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If 2xy + z = 9, what is the value of the positive integer z?

(1) xyz - z^2 = 0 --> $$z(xy-z)=0$$ --> $$z=0$$ or $$z=xy$$. Since given that z is a positive integer, then discard $$z=0$$ and we are left with $$z=xy$$. From $$2xy + z = 9$$ we get that $$2z + z = 9$$ --> $$z=3$$. Sufficient.

(2) x + y - 3z = -5. We cannot solve for z. Not sufficient.

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Re: If 2xy + z = 9, what is the value of the positive integer z? [#permalink]  05 Mar 2015, 16:18
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Re: If 2xy + z = 9, what is the value of the positive integer z?   [#permalink] 05 Mar 2015, 16:18
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