FSA: intercorporate investment investment, different, summarize, remember, question

needhelp1700

I did some text book question for FSA: intercorporate investment: about equty method, proportionate consolidation and consolidation:
I remember it said that under all three method, NI and Equity are the same.
But if work through those questions, it looks like the equity and NI could be different.
So can we summarize that: if aquire price = book value of equity and there is no goodwill, then NI and Equity will be the same under all three method?
I still don’t get how NI will be the same under all three method? Thanks.