Let me try..

I dont think I can give a mathematical equation to prove that option B is sufficient but the explanation is logical.

Any number (positive or negative) when raised to an even power gives a positive number.

From equation B :
x + y > z

Therefore, when x and y and z are raised to the same EVEN number, irrespective of the polarity of x,y or z the following holds true: x^4 + y ^4 > z^4

However from equation A: X^2 + Y^2 > Z^2

one cannot deduce the polarity of the x, y or z

Therefore B is sufficient to say that x^4 + y ^4 > z^4


Hope it makes sense.

Instead of solving the inequalities, I tried taking some sample values

1. x^2 + y^2 > z^2

If x^2 = 4 , y^2 = 9 and z^2 = 10 then
X^4 + Y^4 > Z^4

But if x^2 = 0.81 , y^2 = 0.81 and z^2 = 1.60 then
X^4 + Y^4 < Z^4

Statement 1 is not sufficient.

2. x+y > z

If x = 1 , y = -2 and z = -2 then
X^4 + Y^4 > Z^4

But If x = -1, y = -2 and z = -4 then
X^4 + Y^4 < Z^4

Statement 2 is not sufficient

I think the question can be answered by combining both the statements, because if both stmt 1 and stmt 2 are true then X^4 + Y^4 > Z^4 has to be true, otherwise either one of the statements will not hold. Don't have the patience to write the sample values i tried

Am I missing anything?