1. Junhee, doesn't "dangeun" mean a carrot?

2. Yes, A carrot is "dangeun" in Korean.

3. I'm confused. I asked my friend, Bora, if she liked spicy food, she said, "dangeuniji."

4. What did she mean by that?

5. Oh, she meant "Of course." It's Korean slang.
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Q1: Is #3 correct? Will you look at the second sentence? Is it grammatical? Can we use like that in everyday life? There seemes to be no conjunction there.

Q2: Can we substitute 'mean' for 'meant' in #4?

Q3: Can we substitute 'means' for 'meant' in #5?

2 answers

#3 is not correct. Instead of a comma to separate the clauses, you need either a semi-colon or the conjunction "and": "...spicy food; she said, "dangeuniji." Or, "and she said..."

#2, A is not capitalized.

#5, "means' is present tense, "meant" is past tense. Either might be appropriate in this sentence. She meant it when she said it, or she means that she always likes spicy food (in the present, not the past).
Q1. Yes, 'dangeuniji' means 'Of course'. It's not a polite way to say it to people who elder than you though. You can say it to your friends or people who younger than you.