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A 3.5 and 3.6 respectively is actually much better than you would think, especially for an engineer. It is right at or above average for all Top 10 schools. As far as the GMAT goes, you should definitely shoot for 700+ and preferably 720+. All top 10 schools have average GMATs of 710-730, so you should shoot to atleast be in this range or higher. Something higher will help your profile somewhat, but you just need to make sure to atleast get to that 700 mark.

You should really do some research around the forums, and your desired schools websites to get a feeling for what else a strong applicant brings. GPA, GMAT, and LoR are great to have, but as an applicant you must also bring leadership experience, extra curriculars, stellar essays, solid resume, and great work experience. Right now is a great time to start your journey b/c you can spend a good 3 months or so studying for the GMAT, and be right in time to put together some solid applications for Round 1 applications come next season. Round 1 is the best time to apply, with the best chances, and will give you opportunities to stagger your applications into R1 and R2 if needed.

Take a look at this post: the-bed-wetting-applicant-thread-for-116569.html?fl=menu to see what average stats are at the schools you are considering applying. As far as a study plan, start here: gmat-study-plan-start-your-gmat-journey-80727.html?fl=menu

I would also consider ordering this book: http://www.amazon.com/Complete-Start-Fi ... 1935707000 This will really get you in the right mindset to get into a top 10 school.

Good luck and let us know if you have any questions we can help you out with!
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Not only do you NOT have a low GPA,..but a 3.5/3.6 in Physics and Mech E will probably be considered the equivalent of a 4.0 in some other disciplines as far as adcomms are concerned. The difficulty of the degree is heavily factored in. GPA is not your problem.

Judging from your quant background, I'm sure you'll do awesome in the GMAT quant,......what I suggest strongly is that you immediately buy the Powerscore Logical Reasoning Bible and go through LSAT logical reasoning excercises. I can gaurantee if you do this,..the critical reasoning portion of the GMAT verbal will be a cakewalk. I took that approach and scored a 45 in the verbal (which is 99th percentile). With that strategy you'd have a great shot at hitting well above 700. Best of luck,..the b-school application process is about a lot more than GPA/GMAT,....but GPA/GMAT is certainly the foundation for a good app. And your foundation has the potential to be REALLY strong. As long as you buckle down there is nothing stopping you from getting top 10.