Is the answer (C)?
As soon as I see anything like this, I automatically simply the equation. I get:
A^4 + B^4 =
(A^2 - B^2)(A^2 + B^2) =
(A+B)(A-B)(A^2 + B^2)
Now,
(1) A^2 - B^2 = 16
Insufficient. We have two variables (A & B), and one statement isn't enough to solve for both of them.
(2) A+B = 8
Insufficient. Same reason as above.
(1+2) is sufficient, since we know
A+B=8
A^2 - B^2 = 16 => (A+B)(A-B) = 16, and
Since we know A+B = 8 from (2), we can plug this into statement (1),
(A+B)(A-B) = 16 =>
8(A-B) = 16,
so this must mean
A-B = 2
So we have two equations
A+B = 8
A-B = 2
And can thus easily solve for both A and B, (A=5, B=3), and we can solve for A^4 + B^4. So hence, (1 & 2) is sufficient => Answer C.
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