(a^3)b+(a^2)(b^2)+a(b^3)>0? 1. ab>0 2. b<0

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(a^3)b+(a^2)(b^2)+a(b^3)>0? 1. ab>0 2. b<0 [#permalink]

05 Nov 2010, 09:43

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(a^3)b+(a^2)(b^2)+a(b^3)>0?

1. ab>0
2. b<0

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Re: a^3b+ [#permalink]

05 Nov 2010, 10:26

Creeper300 wrote:

(a^3)b+(a^2)(b^2)+a(b^3)>0?

1. ab>0
2. b<0

Original Statement:

(a^3)b+(a^2)(b^2)+a(b^3) = ab ( a^2 + ab + b^2)

Statement 1:

if ab > 0 then

ab ( a^2 + ab + b^2) ---> greater then 0, sufficient.
(+) (+) (+) (+)

Statement 2:

b < 0 but we do not know is a is > 0 or < 0 so insufficient.

My answer is A

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Re: a^3b+ [#permalink]

05 Nov 2010, 10:42

This is equal to:
ab(a^2+ab+b^2)>0 ?
(1)if we know that ab>0 then we surely can say that the whole left side of the equation is >0. sufficient

(2) b<0 alone is not sufficient to say if the equation is true. If a>0 it could be possible that the equation is <0, if a<0 the equation is >0, if a=0 , the equation is = 0 and not greater than 0. not sufficient

I think it should be A. What is the OA ?

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Re: a^3b+ [#permalink]

09 Nov 2010, 06:41

(a^3)b+(a^2)(b^2)+a(b^3)>0

I simplified to a^2 + ab + b^2 > 0

1) ab>0: all three terms are positive, therefore suf.

2) b<0: for b < -1 then statement is true for all values of a.
for -1 < b < 0 then statement could be true or false dependant and values of a. therefore not suf.

therefore A.

any holes in my analysis?

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Re: a^3b+ [#permalink]

09 Nov 2010, 08:53

Creeper300 wrote:

(a^3)b+(a^2)(b^2)+a(b^3)>0?

1. ab>0
2. b<0

A. This can be simplified to ab(a^2 + ab + b^2) > 0.

(1) ab > 0. We know that a^2 and b^2 are both greater than zero, so we have two positive terms multiplied together - sufficient.

(2) This tells us nothing about a. Insufficient.

Re: a^3b+ [#permalink] 09 Nov 2010, 08:53

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(a^3)b+(a^2)(b^2)+a(b^3)>0? 1. ab>0 2. b<0

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(a^3)b+(a^2)(b^2)+a(b^3)>0? 1. ab>0 2. b<0

(a^3)b+(a^2)(b^2)+a(b^3)>0? 1. ab>0 2. b<0

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