Translation:The cat exists and at the same time does not exist.
It is Schroedinger's cat. The sentence deals with this thought experiment relating to particles physics. (Just to give you the keyword for a Google search; I' m not able to explain further...)
Here's the link to the wikipedia article: https://en.wikipedia.org/wiki/Schr%C3%B6dinger%27s_cat (I was on my phone this morning, and I can't handle linking etc on my phone very well.)
Since Korean has no corresponding word for the, it is sometimes (actually very often) impossible to tell whether it is an apple or the apple that they are talking about, from the context. Then chances are it is an apple, as it is normal to use 그 in lieu of the in such cases.
This is the reason why most of the translations on Duolingo are missing the the/a equivalent translations when both are correct. The best a student can do is remember the other correct translation when Duolingo states that the your correct translation is wrong. At this point the missing the/a equivalent translations are probably the biggest category of translations missing in this Duolingo course.