There is a special discussion thread for this question:gmat-diagnostic-test-question-79340.html
Please ask your question in that thread. I see that you have to plug the values from the answer choices in order to get the right answer.
The jist of the Questions
A$B = A+B if A>B , and A$B = B-A if , B>A
"In short, the value of the operation is equal to 2A"
I cant get my head wrapped around this ... grateful if someone can throw in some more flavor
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