In hiring, one of the biggest mistakes you can make is hiring people who are well spoken, but can't get the job done. It's easy to make because an interview is a mostly verbal experience, and one assumes that eloquence => competence, which is often not the case.
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Different types of intelligence are almost always correlated, naturally, but to your point, if someone is a good talker, they may choose not to invest in other skills because they see the power of bullshit, which could lead to an inverse relationship, paradoxically.
