Your calculations look good to me. The problem is that you are answering a different question. The question asks "By what percent is candidate X expected to win?" I'm not crazy about the wording of this question, but let's look at an example.
If A gets 40% of the votes, and B gets 60% of the votes, we COULD says that B got 50% more votes than A got. ORRRRR we COULD say that B won by 20%. Based on the official answer, the question's author is using the latter.

Here's one approach:

Let's go with 30 registered republicans and 20 registered Democrats (for a total of 50 voters), and do our calculations.

For Candidate X
80% of 30 + 15% of 20 = 24 + 3 = 27

For Candidate Y
There are 50 voters altogether. If 27 vote for Candidate X, then the remaining 23 must vote for Candidate Y (50 - 27 = 23)

Now let's examine the election results.
Candidate X: 27/50 = 54%
Candidate Y: 23/50 = 46%

Candidate X wins by [spoiler]8% [/spoiler]
Answer: C

Cheers,
Brent

Hi shibsriz,

Your approach to this question was great (it's the same way that I would have dealt with it).

If a question expects you to use the Percentage Change Formula, it will use a phrase such as "percentage change", "percent increase" or "percent decrease."

This question didn't use any of those phrases, so I have to assume that we're NOT supposed to use that formula. Elections, much like sporting events, are won by a "difference of the scores." When a soccer team wins a game 3 to 1, then that team "won BY 2 goals."

In this question, Candidate X received 54% of the vote while Candidate Y received 46% of the vote. Thus, Candidate X won the election by 8% of the voters.

GMAT assassins aren't born, they're made,
Rich