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

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Director
Joined: 08 Feb 2007
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If 2xy + z = 9, what is the value of the positive integer z? [#permalink]

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23 Jul 2007, 07:49
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If 2xy + z = 9, what is the value of the positive integer z?

(1) xyz – z2 = 0

(2) x + y – 3z = -5

Will post OA later.

Kudos [?]: 18 [0], given: 0

Senior Manager
Joined: 04 Jun 2007
Posts: 345

Kudos [?]: 33 [0], given: 0

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23 Jul 2007, 07:56
lanter1 wrote:
If 2xy + z = 9, what is the value of the positive integer z?

(1) xyz – z2 = 0

(2) x + y – 3z = -5

Will post OA later.

A for me.

stmt 1: z(xy-z) = 0
Since z is a positive integer, xy = z. Sufficient.

stmt 2: clearly insufficient.

Kudos [?]: 33 [0], given: 0

Director
Joined: 08 Feb 2007
Posts: 609

Kudos [?]: 18 [0], given: 0

Location: New Haven, CT

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23 Jul 2007, 08:39
In the equation z(xy-z)=0, can't z=0 or z=xy. This would give two different values. This is where I am confused.

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Senior Manager
Joined: 04 Jun 2007
Posts: 345

Kudos [?]: 33 [0], given: 0

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23 Jul 2007, 08:53
lanter1 wrote:
In the equation z(xy-z)=0, can't z=0 or z=xy. This would give two different values. This is where I am confused.

z cannot be 0 since the question stem says that z is a positive integer. Zero is neither positive or negative.

Kudos [?]: 33 [0], given: 0

Director
Joined: 08 Feb 2007
Posts: 609

Kudos [?]: 18 [0], given: 0

Location: New Haven, CT

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23 Jul 2007, 09:42
Wow...i guess i completely missed that. stupid mistake.

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23 Jul 2007, 09:42
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