ㄴ지

wraps an embedded question: what/whether

Folds a question inside a bigger sentence: 뭔지 아세요? is "do you know what it is?", 얼마나 부자인지는 중요하지 않아요 is "how rich you are doesn't matter", 몇 신지 맞춰 보실래요? is "can you guess what time it is?". Whatever question word the clause holds — what, who, how much — stays in place, and this ending simply seals the clause so verbs like 알다, 모르다, or 궁금하다 can take it. Paired up it gives "whether or not": 맞는지 틀린지 is "whether it's right or wrong". It is not itself a question ending; the sentence's real ending comes later.