Greetings. I would like to know my chances at a top 20 school with the following credentials?

1) 620 (Q40 V35)
2) 3.4 GPA from a top twenty university in the US
3) 3.5 years of work experience at a large investment bank. Worked in a corporate development analyst program and got promoted to Associate. On track to become VP within a few years.

I would like to apply to schools such as Johnson and Tepper. Will also look to take the GMAT again.

I'd say your chances are low at this point, since the average GMAT scores at Johnson and Tepper are around 700. Plus, you're under the average in terms of work experience, which tends to be around five years for both schools.

If you get your GMAT score up to 720 or so you'd have a much, much better chance. At this point any school in the top 20 is a reach.