Hi mathez11,
Unless the application at any of these programs specifically states that a Q51 is "required", you don't need a Q51. These are really competitive programs (obviously), and the Admissions Officers at each will look at your OVERALL APPLICATION (and nitpick it). If you applied and got rejected, it's won't likely be because of your GMAT score.
That all having been said, your missing points are not likely to be found in one category - they're going to be found in the little mistakes that you make throughout the section. Take a good look at your last CAT - of all the Quant questions that you got wrong, how many were because of a silly/little mistake and how many were because the question was just too hard? I bet more of them fall into the first category than the second. THOSE are the issues that you have to fix if you want to raise your Quant score. Usually it's an issue of 'mechanics' - you're not taking enough notes and/or you're doing too much work 'in your head.'
GMAT assassins aren't born, they're made,
Rich