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Data Sufficiency Math Problem

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Data Sufficiency Math Problem [#permalink] New post 26 Jan 2010, 15:16
What's the value of a^4 - b^4 ?

1. a^2 - b^2 = 16

2. a + b = 8

Appreciate it if somebody can help me in solving the above DS problem. An explanation will also be appreciated.

Thanks
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Re: Data Sufficiency Math Problem [#permalink] New post 26 Jan 2010, 15:26
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amadi4040 wrote:
What's the value of a^4 - b^4 ?

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

2. \(a + b = 8\)

Appreciate it if somebody can help me in solving the above DS problem. An explanation will also be appreciated.

Thanks

IMO C.

\(a^4 - b^4 = (a^2 - b^2)*(a^2 + b^2)\)

1. \(a^2-b^2 = 16\). Clearly insufficient as we do not know the value of \(a^2+b^2\).
2. \(a+b = 8\). Again insufficient as it does not provide any information about value of \(a-b\).

Together 1 and 2 are sufficient. How???
\(a^2-b^2 = 16\)
\((a-b)*(a+b) = 16\)
\(a-b = 2\) As we know that \(a+b = 8\). Now we can find the value of \(a & b\).

Thus answer is C.
Re: Data Sufficiency Math Problem   [#permalink] 26 Jan 2010, 15:26
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