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# Is A^3*B^2*C^3>0 1.BC<0 2.AC>0

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VP
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16 Feb 2008, 04:15
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Is A^3*B^2*C^3>0

1.BC<0
2.AC>0
Director
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16 Feb 2008, 06:55

In the original question stem B will always be positive. Meaning we're really only concerned about A and C. Statement 2 tells us that AC>0, so A and C have the same sign. It doesn't matter which sign it is. If they're negative, they'll have a positive product. If they're positive they'll have a positive product. Then B is positive, so yes, A^3*B^2*C^3 is greater than 0.
VP
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16 Feb 2008, 08:00
eschn3am wrote:

In the original question stem B will always be positive. Meaning we're really only concerned about A and C. Statement 2 tells us that AC>0, so A and C have the same sign. It doesn't matter which sign it is. If they're negative, they'll have a positive product. If they're positive they'll have a positive product. Then B is positive, so yes, A^3*B^2*C^3 is greater than 0.

you forget about the case in which B=0
SVP
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16 Feb 2008, 08:22
gah, read the question wrong as A^2 instead of A^3 !!! That rightly messed things up for me.

Upon further consideration, B is right
Director
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16 Feb 2008, 09:25
marcodonzelli wrote:
eschn3am wrote:

In the original question stem B will always be positive. Meaning we're really only concerned about A and C. Statement 2 tells us that AC>0, so A and C have the same sign. It doesn't matter which sign it is. If they're negative, they'll have a positive product. If they're positive they'll have a positive product. Then B is positive, so yes, A^3*B^2*C^3 is greater than 0.

you forget about the case in which B=0

Ahhh, good call. We need to know that B is not = to 0.

C it is. Good catch
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16 Feb 2008, 11:17
Wrong.
C.

2) Tells you A & C are both negative or positive, along with not being equal to 0.

But, you don't know if B is 0 or not. If B is not 0, then yes, the equation is larger than 0. However, B can be 0, in which case the equation is equal to 0, and it is not bigger than 0.

1 & 2 together tell you that B is non-null.
Re: inequalities   [#permalink] 16 Feb 2008, 11:17
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