There are three possible answers to the question because it is ambiguous. It depends how you interpret it. There may be a typographic error in the question because it ends with “how many cat remains?”. In this phrase the word “remains” would mean carcasses or dead bodies. So if we take the question on face value and that the word “cat” in this section of the question is meant to be in the singular, the answer is 14.
If this section of the question should read “how many cats remain”, the answer depends upon what the man did with the dead cats. If he’s got them in a freezer then he still has 30 cats, 16 of which are alive and 14 of which are dead.
If the man has buried or cremated his 14 dead cats then 16 of them remain with him.
As you can see there are three possible answers one of which depends on deciding whether the question contains a typographic error.
The question was asked on Quora.com. In my opinion the question is deliberately asked in an ambiguous way. It has to be ambiguous because if not the answer is too easy. The whole point of the question is to challenge the way it has been asked as I have done. In the original question the cat owner is a lady. I have changed this in the hope that Google might rank the page higher in search results. There is no other reason.