Data Sufficiency

M7MBA wrote: ↑

Wed Feb 23, 2022 8:17 am

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.

Answer: C

Source: Official Guide

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