Translation:We are looking for an apartment which is cheaper.
I don't think it's as simple as that. This is a quote from Oxford Dictionaries (https://en.oxforddictionaries.com/usage/that-or-which): "Note that in British English, the word which is often used interchangeably with the restrictive that:
✓ She held out the hand which was hurt."
So it seems to me that Duo's translation might very well be fine in British English.
I think in English it would depend upon the intent. These two constructs would, to me, imply different things:
a) "We are looking for an apartment which is cheaper." (restrictive clause, no comma)
b) "We are looking for an apartment, which is cheaper." (non-restrictive clause, offset by comma)
The first one means that you're looking for an apartment which is cheaper than your existing apartment, or perhaps cheaper than one you're currently viewing in an ad. A cheaper apartment is what you're looking for, and that's essential to the sentence. So for example it might come in this context:
a) "Our existing apartment is raising the rent. We are looking for an apartment which is cheaper."
The second one means you're contrasting an apartment with some other different mode. Perhaps you're comparing it to a house, or renting a hotel for a long visit. In this case the adjectival clause clarifies the situation, but it doesn't add any essential info to "apartment".
b) "We are staying for a month so a hotel is too expensive. We are looking for an apartment, which is cheaper."
Now, do most native speakers even follow this rule? Or would grasp the difference? That's open to doubt. :)
"We are looking for a cheaper apartment" not accepted in 04/01/2020. I have reported it but I've also just read Zegator's point below and see the logic. I'm afraid I'm having a block to words like non/restrictive clauses which I'm sure I'll get someday; I think I need a break!
Although "We are looking for a cheaper apartment" and "We are looking for an apartment which is cheaper" both carry the same meaning, the former does not demonstrate and reinforce the use of relative pronouns. So, for advanced learners, who have already mastered the basic concepts of using relative pronouns, it's not so important to answer with the latter. For beginners (whether in German overall or only on the topic of relative pronouns), an effective way for die Eule to know whether they "get it" is to require the use of relative pronouns in the English answer.
Perhaps the developers could program a means to allow certain alternative answers to be acceptable for advanced learners but not beginners. This would probably require a significant increase in resources to add/mark answers in that fashion.
Wir suchen eine billigere Wohnung = We are looking for a cheaper apartment.
Wir suchen eine Wohnung, die billiger ist = We are looking for an apartment which is cheaper.
The two mean more or less the same thing but they are grammatically different; it's best to stick with the grammar the German uses (adjective versus relative clause).
Requiring the use of relative pronouns in the English answer is an effective way for die Eule to assess whether a user understands the use of relative pronouns. If this were a construct that didn't exist in one or the other language, then obviously it wouldn't be required, but the similarities between German and English permit this as a means of teaching/reinforcing the concept.
Duolingo is very inconsistent with this sort of translation difference. In English, the two are completely interchangeable, so either correct English translation of the German sentence should be accepted. In an English course, it would be reasonable to specify which form of the English version should be allowed, but not in a German course.
And of course, Duolingo doesn't make those sorts of specifications of form anyway. (I think it probably should.)