Quant trader straight out of undergrad? Or am I being foolish

I've scoured WSO and google searches on becoming a quant straight out of undergrad, and it seems either of these 2 things:

1) Major in applied mathematics and/or computer science
2) Get a PhD or go to grad school in a mathematics and computer-science intensive field

Would I still have a chance if I majored in Finance and minored in either applied mathematics or computer science? Or is it absolutely necessary to major in these two fields?

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