Thanks for the message. It sounds like you have a strong level of work experience and job progression. It’s also good that you have some finance experience given your desire to shift to IB or PE.
In terms of your target schools, with your current profile I would recommend looking at schools ranked in the top 15-25 in US News and World Report. With a 620 GMAT, these schools are within your range, given that you are in a very competitive demographic pool.
I would suggest retaking the GMAT if time allows, increasing your score to high 600s or low 700s will put schools in the top 10 within your reach, assuming that you had a strong university performance.
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MBA Prep School
San Francisco, CA