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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] New post 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] New post 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.

Answer: A.
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Re: If 2xy + z = 9, what is the value of the positive integer z? [#permalink] New post 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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