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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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If 2xy + z = 9, what is the value of the positive integer z? [#permalink]  14 Nov 2015, 15:58
If 2xy + z = 9, what is the value of the positive integer z?

(1) xyz – z^2 = 0

(2) x + y – 3z = -5
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Re: If 2xy + z = 9, what is the value of the positive integer z? [#permalink]  14 Nov 2015, 22:20
Expert's post
stoy4o wrote:
If 2xy + z = 9, what is the value of the positive integer z?

(1) xyz – z^2 = 0

(2) x + y – 3z = -5

Hi,

1) statement one gives us xyz – z^2 = 0
or z(xy-z)=0..
so either z=0 or xy=z or xy=z=0..
here it is given that z is a positive integer, so z cannot be 0..
xy =z

substitute in main Q, we get value of z as 3.. suff

2) x + y – 3z = -5..
three variables and two equations... in suff

ans A
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Re: If 2xy + z = 9, what is the value of the positive integer z? [#permalink]  15 Nov 2015, 02:40
1) z(xy-z)=0
z≠0 as z is +ve, xy=z
2xy+z=9
Or 3z=9
Or z= 3….sufficient.

2)….not sufficient

ANS: A
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Re: If 2xy + z = 9, what is the value of the positive integer z?   [#permalink] 15 Nov 2015, 02:40
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