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What is the value of a^3-b^3? 1) a^2+ab+b^2=0 2) a-b=3b Many

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What is the value of a^3-b^3? 1) a^2+ab+b^2=0 2) a-b=3b Many [#permalink]

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24 Dec 2005, 06:56
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What is the value of a^3-b^3?

1) a^2+ab+b^2=0
2) a-b=3b

Many thanks!
SVP
Joined: 24 Sep 2005
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Re: Pls help DS questions a^3-b^3 [#permalink]

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24 Dec 2005, 07:19
tennis25 wrote:
What is the value of a^3-b^3?

1) a^2+ab+b^2=0
2) a-b=3b

Many thanks!

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

1. a^2+ab+b^2= 0 --> S= 0 -->suff
2. -->a= 4b --> a^3-b^3= 64b^3- b^3= 63 b^3
we don't know b --> can't calculate S -->insuff

A it is.
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24 Dec 2005, 07:38
Laxie, you know a rule for factoring the bins?

For example

a^3+b^3=?
or
a^4-b^4=?

Thx
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24 Dec 2005, 07:40
Laxie, you know a rule for factoring the bins?

For example

a^3+b^3=?
or
a^4-b^4=?

Thx

a^3+b^3 = (a+b)(a^2 -ab +b^2)
a^4- b^4= (a^2- b^2) ( a^2+b^2) = (a-b)*(a+b)*(a^2+b^2)
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24 Dec 2005, 14:09
a^3 - b^3 = (a-b)(a^2+ab+b^2)

from i) we know (a^2+ab+b^2) = 0, a^3-b^3 = 0 --> Suff
ii) states a-b =3b, i.e a =4b, so a^3-b^3 = 63b^3, --> Insuff

I go with A
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Re: Pls help DS questions a^3-b^3 [#permalink]

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26 Dec 2005, 01:32
tennis25 wrote:
What is the value of a^3-b^3?

1) a^2+ab+b^2=0
2) a-b=3b

Many thanks!

a^3-b^3 = (a-b)(a^2+ab+b^2)
= (a-b) * 0
= 0 Hence suff.

From Stmt 2 we get a = 4b, so a^3-b^3 = 64b^3-b^3
= 63b^3, b could be any number hence insuff.

So A.
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01 Jan 2006, 03:57
Thanks so much for your help all. And a very Happy New Year to you all!
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