This is my experience after working at quite a few large companies over the last 4 years since uni.
You should optimise for passing the pub test not the programming test, and you probably don't want to work at a place that hands out codility tests.
Here's some anecdotes from my hiring experience:
My team and I once rejected a lad because we thought he would get bored after a couple of weeks. He got 100% in his codility, flawless technical interviews etc... He was too good for us and our trivial domain (this was a FTSE100, our services were consumed by 90% of the companies teams, in a very buzzwordy area).
Same company: two candidates, the first was technically better than the second. However no one who spoke to the first said they would be keen to go for a pint with him. The second was an absolute mensch so he got the job. He even said in the interview that he thought it was going terribly...
Once I interviewed two Devs on the same day, HR sent the offer to the wrong one and he accepted. Our team didn't know until he turned up on Monday morning.
Before my current gig I interviewed for a contract at a startup. The product was simple: just applying tech to a sector that is all man power based at the moment. This was the hardest technical interview I've ever had to give. I was asked to write the longest common subsequence algorithm. I did not write one line of code: eventually it turned into me watching the interviewer write the code. I was sure it was a disaster. The guy said he loved me, and wanted me to do the 'pairing' test again... All because of the pub test. I declined.
The interview for my current gig was a 30 minute chat on Skype. A team mate told me it was between me and another, but he was boring.