Hi varmasneha91,
If you're certain that you want to take the Official GMAT during the first week of June, then there's a pretty good chance that you will have to take the At-home Exam. Thus, going forward, you should plan to take your practice CATs under the same parameters (use an online notepad - not handheld notes, take the sections Q/V/IR in that order with no 'break' until after the Verbal section, etc.). Based on your current timeframe, you have about 5 weeks of potential study time - but many people are finding the At-home testing conditions make taking the GMAT a bit more challenging - meaning that you might end up needing more study time to hit your Score Goal than you have currently allotted.
Based on your current practice CAT Scores, you can pick up the additional points that you are after in a variety of ways - so you don't necessarily need to score a lot higher in either section. You might find it more practical to focus more on the Verbal section though (since you have a much greater opportunity to pick up more points there).
1) Are you working with any specific study materials right now or are you just working through sets of practice questions?
2) Going forward, are you planning to continue studying approximately 20 hours a week?
GMAT assassins aren't born, they're made,
Rich