Did candidate x receive more than half of the 30,000 votes cast in the

Target question: Did candidate x receive more than half of the 30,000 votes cast in the general election?

Statement 1: Candidate y received 12,000 of the votes cast
The mistake to be made here is to assume that there are only 2 candidates. However, there is nothing in the wording of the question to suggest this.
In fact, if we examine the two statements, we see that only 25,000 votes are accounted for.

There are several scenarios that satisfy statement 1. Here are two:
Case a: Candidate y received 12,000 votes, Candidate w received 1,000 votes, and Candidate x received 17,000 votes.
In this case, Candidate x received MORE THAN half of the votes
Case b: Candidate y received 12,000 votes, Candidate w received 10,000 votes, and Candidate x received 8,000 votes.
In this case, Candidate x received LESS THAN half of the votes
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: Candidate x received 13,000 of the votes cast.
A total of 30,000 votes were cast.
So, Candidate x DID NOT receive more than half of the votes
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent