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01 Sep 2008, 04:29
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Is \(X^2 * Y^5 * Z > 0\) ?
1. \(\frac{XZ}{Y} > 0\)
2. \(\frac{Y}{Z} < 0\)
1. \(\frac{XZ}{Y} > 0\)
2. \(\frac{Y}{Z} < 0\)
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01 Sep 2008, 06:13
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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.
(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.
01 Sep 2008, 14:36
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arjtryarjtry
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.
