Which is correct: A) "동생이 '난 학교에 안 가겠다'라고 말했다" or B) "동생이 '난 학교에 안 가겠다'고 말했다"?

ANSWER: A

In his book "나의 한국어 바로 쓰기 노트" (My Notes for Correct Korean Usage), one of the things that Mr. Nam Yeong-sin (남영신) writes about is the correct way to write direct and indirect speech in Korean, and one of the first things he does is ask which of the two Korean sentences is correct:

A: 동생이 "난 학교에 안 가겠다"라고 말했다.
A: My younger brother/sister said, "I'm not going to school."

B: 동생이 "난 학교에 안 가겠다"고 말했다.
B: My younger brother/sister said, "I'm not going to school."

He writes that if you want to quote someone, which means to use the person's exact words (direct speech), you must include the postpositional particle -라고 or -이라고 after the quote. But if you just want to report what the person said without using the person's exact words (indirect speech), then you would just use the ending -다고, -ㄴ다고, or 는다고. So, that means Sentence A above would be the correct way to write a direct quotation in Korean. 

If you wanted to simply report what the younger brother or sister said, without using his or her exact words, then you would omit the quotation marks ("...") and the 난 (I'm) and just write 동생이 학교에 안 가겠다고 말했다.

I mention this because I seem to remember reading elsewhere that Sentence B would be the correct way to write a direct quotation. In other words, I read that -라 or -이라 was unnecessary. So, there seems to be some confusion among Koreans about the correct way to quote someone.

I think Mr. Nam is correct because if the direct quote were "난 학교에 안 가겠어요," then 동생이 "난 학교에 안 가겠어요"라고 말했다" sounds much better than 동생이 "난 학교에 안 가겠어요"고 말했다.