gmattesttaker2 wrote:
What is the value of x?

(1) (x)(x + 1) = (2013)(2014)
(2) x is odd

Target question: What is the value of x?

Statement 1: (x)(x + 1) = (2013)(2014)
It's tempting to look at this and conclude that x = 2013.
However, let's look at it this way: (x)(x + 1) = some POSITIVE number
This opens up 2 possibilities: EITHER x and (x+1) are both positive, OR x and (x+1) are both negative.
Now that we've recognized this, can take the fact that the product is (2013)(2014) and use it to our advantage. When we do so, we get exactly 2 possible cases:
Case a: x = 2013 and (x+1) = 2014, in which case x = 2013
Case b: x = -2014 and (x+1) = -2013, in which case x = -2014
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x is odd
No way to determine the value of x
Statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 results in two possible cases: EITHER case a is true, OR case b is true.
Statement 2 tells us that case b cannot be true and that case a MUST be true.
In other words, it MUST be the case that x = 2013 and (x+1) = 2014
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent