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# Is X^2 * Y^5 * Z > 0 ? 1. \frac{XZ}{Y} > 0 2.

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Current Student
Joined: 11 May 2008
Posts: 551
Is X^2 * Y^5 * Z > 0 ? 1. \frac{XZ}{Y} > 0 2. [#permalink]

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01 Sep 2008, 04:29
Is $$X^2 * Y^5 * Z > 0$$ ?

1. $$\frac{XZ}{Y} > 0$$
2. $$\frac{Y}{Z} < 0$$

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VP
Joined: 21 Jul 2006
Posts: 1455
Re: is X*Y*Z>0 [#permalink]

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01 Sep 2008, 06:13
The answer should be C.

(1) if y is negative, then either X or Z must be negative. So if y is negative and Z is negative, then the overall product will be positive. However, if Y is negative and X is negative, then the overall product will be negative because y^5 will be negative and any positive number multiplied by a negative will always be negative.

(2) No information about X. for all we know, X could be a zero.

(1&2) So we know that X is not a zero. But when you consider the different scenarios, the product will always be negative since X^2 will always be positive. So when either X or Z has to be a negative, the overall product will always be negative. We know this because their powers are odd and so it will maintain their original signs.
SVP
Joined: 07 Nov 2007
Posts: 1738
Location: New York
Re: is X*Y*Z>0 [#permalink]

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01 Sep 2008, 14:36
arjtryarjtry wrote:
Is $$X^2 * Y^5 * Z > 0$$ ?

1. $$\frac{XZ}{Y} > 0$$
2. $$\frac{Y}{Z} < 0$$

X^2 * Y^5 * Z >0 --> X^2 * Y^4* YZ>0
--> YZ>0

1) XZ/Y >0

Not suffcieint Z/Y can be -ve or +ve based on X

2) Y/Z<0 means Y and Z must have opposite signs

YZ<0

X^2 * Y^4* YZ>0 is not true

even if X=0 X^2 * Y^4* YZ>0 is not true

So we don't require X value.

I will go with B.

What is OA.
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Director
Joined: 23 Sep 2007
Posts: 761
Re: is X*Y*Z>0 [#permalink]

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01 Sep 2008, 15:05
C

B is not suff because x can be 0, which make the equation $$X^2 * Y^5 * Z = 0$$
if x is not 0, then y and z would come into play.
Director
Joined: 12 Jul 2008
Posts: 512
Schools: Wharton
Re: is X*Y*Z>0 [#permalink]

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01 Sep 2008, 15:44
arjtryarjtry wrote:
Is $$X^2 * Y^5 * Z > 0$$ ?

1. $$\frac{XZ}{Y} > 0$$
2. $$\frac{Y}{Z} < 0$$

C

Here, you need to know whether Y and Z are the same sign and that none of the values are 0.

(1) Insufficient

Tells you that none of the variables are 0 and that XZ and Y are the same sign.

(2) Insufficient

Tells you that Y and Z are the same sign.

(1) and (2) Sufficient
SVP
Joined: 07 Nov 2007
Posts: 1738
Location: New York
Re: is X*Y*Z>0 [#permalink]

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01 Sep 2008, 15:55
gmatnub wrote:
C

B is not suff because x can be 0, which make the equation $$X^2 * Y^5 * Z = 0$$
if x is not 0, then y and z would come into play.

Question is X^2 * Y^5 * Z > 0
when x=0 :X^2 * Y^5 * Z = 0 -- Answer to the question is "NO"
when x<>0 : X^2 * Y^5 * Z < 0 --> Answer to the question is "NO"

Suffcient
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Joined: 21 Jul 2006
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Re: is X*Y*Z>0 [#permalink]

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01 Sep 2008, 16:39
x2suresh wrote:
gmatnub wrote:
C

B is not suff because x can be 0, which make the equation $$X^2 * Y^5 * Z = 0$$
if x is not 0, then y and z would come into play.

Question is X^2 * Y^5 * Z > 0
when x=0 :X^2 * Y^5 * Z = 0 -- Answer to the question is "NO"
when x0 : X^2 * Y^5 * Z Answer to the question is "NO"

Suffcient

hmmm...good point actually because whether X is zero or not, the result will still not be positive. good catch. so i guess the answer is B

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This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

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Re: is X*Y*Z>0   [#permalink] 01 Sep 2008, 16:39
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# Is X^2 * Y^5 * Z > 0 ? 1. \frac{XZ}{Y} > 0 2.

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