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"a^4 - b^4 = ? (Not Hard)

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by The Duke » Mon Aug 09, 2010 8:24 am
For some reason I have difficulty with this question as I'm not getting it.
Can someone work out the algebra for me (thanks)

What does a^4 - b^4 equal ?

(1) a^2 - b^2 = 16

(2) a + b = 8


Answer = C.
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Source: — Data Sufficiency |
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by robby90210 » Mon Aug 09, 2010 8:36 am
simplify it to (a^2 +b^2)(a^2-b^2)

option a - we only a^2 - b^2, so this is not sufficient.

option b - reduce the equation further to - (a^2 + b^2) (a +b) (a -b). we only the value of (a+b).. so this is not sufficient.


combining both options, we know the value of (a^2-b^2) and (a+b).... but not (a-b)..so insufficient.


hence answer is E
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by selango » Mon Aug 09, 2010 8:38 am
a^4-b^4?

we need to know values of a and b


stmt1,

a^2 - b^2 = 16

(a+b)(a-b)=16

No info about a and b.

Insuff

stmt2,

a+b=8

No info about a and b.

Insuff

Combining 1 and 2,

8(a-b)=16

-->(a-b)=2 and (a+b)=8

Solving the 2 equations ,a=5 ,b=3


a^4-b^4=5^4-3^4=544

Suff

Pick C
--Anand--
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by The Duke » Mon Aug 09, 2010 8:49 am
robby90210 .... I did that exact same thing when I did the question & choose E

selango ... much appreciated and C is correct.


I just did not simplify enough to see that values for a and b were indeed attainable, as I was looking at the question stem to much instead of the statements
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