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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
Posts: 2736

Kudos [?]: 1022 [0], given: 4

Location: New York City
X Y and Z are positive integers. Is (X-Y)(Y-Z)(X-Z) > 0? [#permalink]

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15 Dec 2007, 16:36
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0% (00:00) correct 100% (01:36) wrong based on 3 sessions

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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

Kudos [?]: 1022 [0], given: 4

SVP
Joined: 29 Aug 2007
Posts: 2473

Kudos [?]: 832 [0], given: 19

Re: Algebra - Is (X-Y)(Y-Z)(X-Z) > 0? [#permalink]

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15 Dec 2007, 18:56
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.

Kudos [?]: 832 [0], given: 19

CEO
Joined: 29 Mar 2007
Posts: 2554

Kudos [?]: 500 [0], given: 0

Re: Algebra - Is (X-Y)(Y-Z)(X-Z) > 0? [#permalink]

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15 Dec 2007, 22:17
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.

Kudos [?]: 500 [0], given: 0

Intern
Joined: 09 Nov 2009
Posts: 1

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

Re: Algebra - Is (X-Y)(Y-Z)(X-Z) > 0? [#permalink]

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09 Nov 2009, 04:59
x<y<z would make it negative..so the answer to your question is a big NO.

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

Manager
Joined: 23 Jun 2009
Posts: 145

Kudos [?]: 14 [0], given: 9

Re: Algebra - Is (X-Y)(Y-Z)(X-Z) > 0? [#permalink]

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11 Nov 2009, 20:18
Good question,
"D".

Kudos [?]: 14 [0], given: 9

Re: Algebra - Is (X-Y)(Y-Z)(X-Z) > 0?   [#permalink] 11 Nov 2009, 20:18
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# X Y and Z are positive integers. Is (X-Y)(Y-Z)(X-Z) > 0?

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