I was offered two choices, with no English. They want you to say an rèidio 'the radio', although an also means 'their' so it could be 'their radio' (which is not a problem) but the alternative an rèidiothan 'their radios' is grammatically correct and makes sense, so this is not a valid question.
Thank you. Yes. I agree with the first. I don't think there is much dispute about the alienability of radios but the bigger issue is the extent to which people ignore this distinction in conversation.
However, my concern is that you should not be teaching that something is wrong (which is implicit in it being one of the wrong options offered) either on the basis of 'we haven't covered it so you can't use it', or on the basis of a subtle distinction that is not always adhered to and is not the subject of the unit. Nor even on the basis of grammar that has not been practised very much and it not being tested, such as an not being the plural article. Fundamentally, the learner needs to be able to understand why any wrong sentence is wrong or they cannot learn anything, and using either grammar or vocabulary that they have not met does not achieve this.
It is part of a general concern I have that anything that occurs more often (or even exclusively) in the wrong options than in the right options will subconsciously enter the mind as bad Gaelic. In this particular case, rèidiothan has not been used in any valid sentence that I can find, although it is on the vocab list for Sport. So you only encounter it in wrong answers. Further, it is not recognisable to the beginner as a plural - it just looks like a weird word, as -than is not on the list of plural endings.
I presume Duolingo chose it at random from the vocab list, so the solution is either to remove it from the list or to use it in valid sentences.
I have not noticed so much on Gaelic as I generally know the words in the wrong answers, but in Welsh, I have just learnt a list of the words that only ever turn up in the wrong answers, so I don't have to think about the rest of the sentence. Some look so odd that I genuinely thought they were made up as jokes. One was partïon. I didn't even know they had diereses in Welsh. So I got it in my mind this was not a Welsh word. It turned out it was just the Welsh spelling of pàrtaidhean.
So my concern is not really so much to do with obscure grammar as to do with whether the wrong answer helps or hinders the learner. Sorry for going on so long on this.