"Who took a bag?" => 누가 가방을 가져 갔습니까? (there should be no space between 가져 and 갔 but Italki text entry window won't let me write it that way) 누가 가방을 가졌습니까? is grammatically correct but doesn't sound as natural or clear. 가지다's basic meanings are: 1) HAVE in one's possession, 2) CARRY on one's person, 3) MAKE one's own; TAKE. Although meaning (3) might appear to be the same as "take", 가지다 doesn't have the explicit sense of "taking it away". By itself, it just means taking ownership. So 가방을 가졌습니까? sounds like "Who has a bag?" or "Who took possession of the bag?" (the sentence is unclear between these two, so it's not widely used in this form). To express the sense of "to take something", we use 가져가다 (가지다 + 어 + 가다, but it is considered a single word), which is explicitly "take/carry (something) away". As for the 가다 part taking on the past tense, as in 가져갔다, it is how you set the tense of a compound verb. When a verb has two parts, only the last part reflects the tense: 없어지다(없다 + 어 + 지다) -> 없어졌다, 올라가다(오르다 + 아 + 가다) -> 올라갔다, 데리고 가다 -> 데리고 갔다. * Italki turnes 가져 + 갔 + 다 in one word into 가져갔다. So I can't write 갔 correctly. Weird :-)