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

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Manager
Joined: 09 Dec 2006
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If 2xy + z = 9, what is the value of the positive integer z? [#permalink]

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26 Aug 2007, 11:30
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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
VP
Joined: 10 Jun 2007
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26 Aug 2007, 11:40
Piter wrote:
If 2xy + z = 9, what is the value of the positive integer z?

(1) xyz – z^2 = 0

(2) x + y – 3z = -5

I think A.

(1) z*(xy - z) = 0
This equation gives z=0 or xy-z = 0
Since we know z is positive, the latter is the only solution.
so we have xy-z = 0
Multiply that by 2, 2xy - 2z = 0
Substract the given equation with this one, you get:
3z = 9, z=3
SUFFICIENT.

(2) Two equations two unknowns and cannot cancel out, INSUFFICIENT.
Manager
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26 Aug 2007, 12:42
bkk145 wrote:
I think A.

(1) z*(xy - z) = 0
This equation gives z=0 or xy-z = 0
Since we know z is positive, the latter is the only solution.
so we have xy-z = 0
Multiply that by 2, 2xy - 2z = 0
Substract the given equation with this one, you get:
3z = 9, z=3
SUFFICIENT.

(2) Two equations two unknowns and cannot cancel out, INSUFFICIENT.

yeah, you're right
I chose E, 'cause I missed that z is positive, hence I had two solutions for z in (1)
Re: DS integer z   [#permalink] 26 Aug 2007, 12:42
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