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A country run by the learned has a higher chance at being effective than a country governed by all. If the intelligent run the country, then the chances of a democratic mistake go down, because they are intelligent.
There is no true way to tell how intelligent someone is, seeing as there are many different types of intelligence.
It would protect the country from the whims of the unintelligent who have no idea what is good for the nation.
The intelligent could have the means to do good. Will they always have the motive?
If this system was used, it would be fairly easy for a candidate to change the test and have a demographic of voters that agreed with his/her political views.
Past examples of such tests have been struck down, at least in the U.S., for racial discrimination.