We need to determine whether w+h^4 is positive. First, we know that h^4 is always non-negative.
Let’s look at the 2 possibilities for the value of w+h^4:
1) If w is positive, then (w + h^4) will be positive.
2) If w is negative, then h^4 must be greater than |w| in order for (w + h^4) to be positive. For example if w = -4, then h^4 must be greater than 4 in order for (w + h^4) to be positive.
Statement One Alone:
h is positive
Since we already know that h^4 is positive and do not have any information about w, we do not have enough information to answer the question. We can eliminate answer choices A and D.
Statement Two Alone:
w is positive
Since we know that h^4 is non-negative, also knowing that w is positive is enough information to determine that w + h^4 is positive. Statement two is sufficient to answer the question.