It really depends on how much study you need to hit your target score. Most people need at least a few months of intensive preparation. If your target score is significantly higher (150+ points) than your initial practice exam, you may need a longer preparation period.
I wouldn't worry too much about the new section. First off, at this stage it is unlikely to have a significant effect on business school applications. Schools need time to look at the data and figure out what to do with the scores. Even when this has had time to happen (probably after you are safely admitted to a program), the Integrated Reasoning section is not likely to make an enormous difference. Keep in mind that this section will be scored separately from the main test, which is not changing at all. Also, the skills tested in the new section will simply be applications of the material on the main test, so if you start studying now, you will still be preparing yourself for the Integrated Reasoning section.
As for instruction in Singapore, we offer a number of online classes that may fit your schedule. Good luck!
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