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
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