In my first year at university, when I had no choice who I lived with, I shared a house on campus with someone who was so dumb he wouldn't survive outside society.
Obviously he was smart, or at least academically smart enough to be accepted by a fairly prestigious university, yet he was so fucking stupid it beggars belief.
One time he was in his room upstairs and he heard the front door open, so he went onto the landing and leaned over the railing to see who had entered the house... except he leaned over the railing with both hands in his trouser pockets.
Naturally he tipped over the railing and would have fallen to his death if I hadn't left the upstairs bathroom at the exact moment he tipped and managed to grab his ankle and stop him falling.
He was quite shaken up by what had happened, but mainly because he couldn't understand how it had happened, like he lacked the basic understanding of physics and also lacked the basic survival mechanism that would normally prevent a person (or animal) from leaning forward over a sheer drop while all their limbs were restricted.
Another time he couldn't understand why a rose he bough in a bar had withered and died after a week, despite him keeping it in water. We tried to explain that it was already dead, that it wasn't part of the plant and had no roots, that plants need to be planted in soil to get nutrients to live. Then we had to explain what nutrients were and we finally gave up when all he understood was that if he put this dead stem in some dirt, it would come back to life.
Every time he cooked a baked potato in the oven he smoked out the kitchen because he used to butter it before cooking. He just didn't understand that a large knob of butter would change from a solid to a liquid when exposed to heat and that that liquid would drip off a spherical object and burn when it landed on the oven's heating element. No matter how many times it happened and how many times we told him why it was happening and why what he was doing was wrong, he just didn't get it. To him, filling the kitchen with black smoke was part of the process of cooking a baked potato.
He was also very arrogant in him ignorance, proclaiming that he knew everything, therefore if he didn't know it, it wasn't true.
Whenever he cooked something in the oven, he timed it by switching the Microwave on for the same amount of time so that the ping of the Microwave timer would indicate his oven food was ready.
We told him that he couldn't do that because it would damage the Microwave, but because he couldn't grasp the concept of radiation and how Microwaves worked, he didn't believe us. He also wouldn't accept that putting a fork in the Microwave while he turned it on was a good compromise, again because he didn't accept the hocus-pocus science behind what we were telling him.
The only way he finally accepted it was when we went to great lengths to find the instruction manual for the Microwave and show him in black and white where it clearly stated do not operate with nothing inside and do not put metal objects in the microwave, but even then he was still openly sceptical about our scientific reasoning behind what we told him and didn't accept the concepts of radiation, microwaves and electricity.
So yes, in my experience it is possible for someone to be smart yet have absolutely no common sense at all.