Hey raalexan - bummer about not scoring as high as you wished - that test is hard!!! Your question is an important one too. We cover the "to apply or not to apply" question in detail on the EssaySnark blahg, you may want to start here with a few articles:
(By "Round 3" we mean "the last round" - so for Rice we actually mean "Round 5"!)
It sounds like you're targeting the part-time MBA, which means that the adcoms are going to be more flexible with evaluating their candidates (P/T programs are always less competitive than F/T MBA). It also means that you can realistically apply even in the last round and still have a chance.
Here's a post about that:
However, with your GMAT score at 100 points lower than the averages, you'd be pushing it a bit. The good news is that you're doing OK with the quant side. If you take the test again and improve your performance with verbal, it will have a disproportionate effect on the total - in other words, you only have to bump the verbal up a little and you'll be able to get > 600.
What we recommend is first, contact the schools and talk to someone in admissions. See what they say. They will be a good resource for you. If they indicate that you should take the test again, then that's your answer. The schools aren't always definitive on such questions but sometimes with these part-time programs they'll do a pre-application consult with a candidate and they sometimes do give clear direction like this. They won't be able to say for sure that they can admit you, but they may be able to say if the current GMAT is just too low to bother with.
If you're not getting clear answers from them, then we would go ahead and retest. In order to have a higher chance at this, then a GMAT above 600 is going to help you significantly. It's not impossible to get in with your current score, but you're making it harder on yourself than needed. If you can get the new test done quickly, then you'd probably be fine in going for one of these part-time programs even in their final round (not true of a full-time program though).
The best chances of course are in Round 1 every year, but it all depends on your personal situation, your reasons for why you want to do the MBA, and when you want to begin. You could still have a shot with a higher GMAT in the last round but we wouldn't risk it with the current score.
Hopefully that helps!! Please stop back by and let us know what you decide to do.
EssaySnark