Data Sufficiency

What is the sum of a certain pair of consecutive odd integers?
(1) At least one of the integers is negative.
(2) At least one of the integers is positive.

Target question: What is the sum of a certain pair of consecutive odd integers?

Some examples of pairs of consecutive odd integers include -7 & -5, -13 & -11, 21 & 23, -1 & 1 etc.

Statement 1: At least one of the integers is negative.
So, one of the odd integers could be negative, or both of the odd integers could be negative.
There are several pairs of integers that meet this condition. Here are two:
Case a: the numbers are -3 and -1 in which case the sum is -4
Case b: the numbers are -1 and 1 in which case the sum is 0
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: At least one of the integers is positive.
So, one of the odd integers could be positive, or both of the odd integers could be positive.
There are several pairs of integers that meet this condition. Here are two:
Case a: the numbers are 5 and 7 in which case the sum is 12
Case b: the numbers are -1 and 1 in which case the sum is 0
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined:
In order to satisfy the conditions in statements 1 and 2, it MUST be the case that one of the odd integers is negative, and the other integer is positive.
The only way that this can happen is when the two integers are -1 & 1
So, the sum of the two integers must be 0

Since we can now answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent

Abhijit K wrote:What is the sum of a certain pair of consecutive odd integers?
(1) At least one of the integers is negative.
(2) At least one of the integers is positive.

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.

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.

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 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.

Answer: C