To be honest, I am not very familiar with PhD programs in management. I know that the competitive nature of these programs is not as frothy as the top 10 or 15 business school programs in the US.
What I have seen is that the applications to PhD programs are generally shorter in nature and focus more on your academic performance. I also know that they generally require a statement of purpose, rather than a set of essays.
The overarching purpose of a PhD program is centered on research. So they are going to want to see evidence of prior work. Do you have this? This is a question that only you can answer. If so, and with a solid GMAT score, and based on my limited knowledge of PhD programs, I do not see why it would be impossible to gain entry into a top 20 program.
I hope this helps.
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