It's often thought that having a precision focused skill set is the way to get ahead, because you can show off how clever you are, but those with a wide spread of skills may make better employees.
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That's the thinking of LinkedIn's Reid Hoffman, who cites hiring people with specific skills, rather than generalists, as one of the big three mistakes he made at an earlier company, SocialNet.
What he learned, however, was that there's a need for those with general skill sets, because companies evolve over time, and being good in just one area might not cut it if your company changes over time, which it certainly will.
So how can you adapt this to your own career? If you've got general skills, tout them, and point out how they demonstrate flexibility to change in the work environment when going for a new job. If you've got specific skills, it's fine to mention them, but try to phrase it around how they could be applied in more general application methods.