They'd have to be at least a relatively sharp tool in the Imperial shed, given the vast array of tactics they have to know and retain, and the complex wargear and power armour they have to come to terms with using. It would be far more intellectually demanding than your average Imperial Guardsman's work (possibly barring Stormtroopers), even with IG being the top of the PDF heap.
However, intelligence will vary between marines. I believe that in the 5th ed SM book, it said that some battle-brothers were "deemed unsuitable" for advancing to Tactical Marine status, and remained a Devastator or Assault Marine. Intelligence levels may play a part in this.
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