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# X Y and Z are positive integers. Is (X-Y)(Y-Z)(X-Z) > 0?

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CEO
Joined: 21 Jan 2007
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Location: New York City
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X Y and Z are positive integers. Is (X-Y)(Y-Z)(X-Z) > 0? [#permalink]  15 Dec 2007, 15:36
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Question Stats:

0% (00:00) correct 100% (01:36) wrong based on 2 sessions
X Y and Z are positive integers.
Is (X-Y)(Y-Z)(X-Z) > 0?

1. X^2 + YZ = XY + XZ
2. XY - Y^2 = XZ - YZ
SVP
Joined: 29 Aug 2007
Posts: 2493
Followers: 59

Kudos [?]: 579 [0], given: 19

Re: Algebra - Is (X-Y)(Y-Z)(X-Z) > 0? [#permalink]  15 Dec 2007, 17:56
bmwhype2 wrote:
X Y and Z are positive integers.
Is (X-Y)(Y-Z)(X-Z) > 0?

1. X^2 + YZ = XY + XZ
2. XY - Y^2 = XZ - YZ

1. x^2 - xy = xz - yz
x (x-y) = z (x - y)
x = z
suff.

2. XY - Y^2 = XZ - YZ
y (x - y) = z (x - y)
y = z

suff.

D.
CEO
Joined: 29 Mar 2007
Posts: 2585
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Re: Algebra - Is (X-Y)(Y-Z)(X-Z) > 0? [#permalink]  15 Dec 2007, 21:17
bmwhype2 wrote:
X Y and Z are positive integers.
Is (X-Y)(Y-Z)(X-Z) > 0?

1. X^2 + YZ = XY + XZ
2. XY - Y^2 = XZ - YZ

1: X^2-XZ=XY-YZ -> X(X-Z)=Y(X-Z) X=Y So suff b/c one of the above terms will be 0.

2: XY-XZ=Y^2-YZ --> X(Y-Z)=Y(Y-Z) X=Y

again one of the above terms will be 0.
Intern
Joined: 09 Nov 2009
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Re: Algebra - Is (X-Y)(Y-Z)(X-Z) > 0? [#permalink]  09 Nov 2009, 03:59
x<y<z would make it negative..so the answer to your question is a big NO.
Manager
Joined: 23 Jun 2009
Posts: 155
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Kudos [?]: 8 [0], given: 9

Re: Algebra - Is (X-Y)(Y-Z)(X-Z) > 0? [#permalink]  11 Nov 2009, 19:18
Good question,
"D".
Re: Algebra - Is (X-Y)(Y-Z)(X-Z) > 0?   [#permalink] 11 Nov 2009, 19:18
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