Hi Karan911,
While I understand why you're upset by this situation, there's a pretty good chance that it had no real impact on your Score results - and won't actually impact your applications in any material way. You're actually asking about a couple of different subjects, so let's start with the immediate issue.
It's certainly possible that having one more correct answer at the end of the section could increase your Scores a little (MAYBE you could have ended up with a Q47 and a 720... but then again, maybe not). However, that assumes that you actually had the correct answer AND that it was not an 'Experimental' question (re: the ones that do NOT count towards your Score). Considering both of those 'unknowns', the probability that you actually lost points as a result of not receiving credit for answering the last question is relatively low.
The second issue is whether you should apply for Round 1 or Round 2 - and that's really a far broader discussion than whether your last Quant question impacted your Score or not. At face value, with a 710/Q46, you can apply to just about any Schools/Programs that interest you. You might run into some issues with Finance-based Programs, but if your OVERALL profile is strong, then the Q46 wouldn't necessarily keep you from earning an invite. Since you know the specific Schools that you plan to apply to, you would likely find it beneficial to speak with an Admissions Expert about your overall profile and plans. Those Experts should be able to answer your Admissions questions and help define the specific areas of your profile that could use some improvement. There's a Forum full of those Experts here:
https://gmatclub.com/forum/ask-admissio ... tants-124/In addition, you could potentially take the GMAT a 3rd time AFTER you have already submitted your application(s). Many Schools will allow Applicants to provide supplementary information to their submissions after the fact (if it's something noteworthy - such as a promotion, receipt of an Award or other 'honor' or a significantly higher Test Score). As such, IF you really want to retest, then you don't necessarily have to do so in the short term.
GMAT assassins aren't born, they're made,
Rich