Low Emotional Intelligence but "High" Intrsonal intelligence? Is it possible?

There are exceptions to everything, scoring low on emotional intelligence probably means that you think mostly out of logic and you don't act or react out of emotion. I think a person whom has been hurt many times as a child develops this decision making style (they have learned to prevent hurtful things by not allowing emotions into the decision making process). You think of others wants and needs and not yours.