# Solution:

We must determine the sum of a pair of consecutive odd integers.

Statement One Alone:

At least one of the integers is negative.

Using the information in statement one, we do not have enough information to answer the question. The two consecutive odd integers could be -1 and 1, with a sum of 0, or they could be -3 and -1, with a sum of -4. Statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

At least one of the integers is positive.

Using the information in statement two, we do not have enough information to answer the question. The two consecutive odd integers could be -1 and 1, with a sum of 0, or they could be 1 and 3, with a sum of 4. Statement two alone 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 know that at least one of the integers is negative and that at least one of the integers is positive. The only pair of consecutive odd integers that includes one negative integer and one positive integer is -1 and 1, with a sum of 0. This is sufficient to answer the question.