We need to determine whether the product zp is negative.
Statement One Alone:
pz^4 < 0
Using the information in statement one, we see that z^4 is positive; whether z is negative or positive, when we raise it to an even power, in this case 4, the result will be a positive number. We can thus determine that p is negative, since the product of a negative and a positive is always negative. However, we still do not know the sign of z itself, because z could be either positive or negative. Thus, the product zp could be either negative or positive. Statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.
Statement Two Alone:
p + z^4 = 14
Using the information in statement two, we see that zp can be either positive or negative. For instance, p = 13 and z = 1 (giving us a positive product for zp) or p = 13 and z = -1 (giving us a negative product for zp). Thus, statement two is not sufficient to answer the question. We can eliminate answer choice B.
Statements One and Two Together:
Using the information from statements one and two we still do not have enough information to determine whether the product zp is less than zero. Knowing that p is negative in statement two doesn’t change the fact that z is still raised to an even power and therefore could still be positive or negative.