There are a few factors that would influence a boards decision.
What boards generally look for is to see that after closing you still have at least 2 years of carrying costs. Since you will be buying all cash, that means if you take the maintainence and multiply it by 24 you would need to have at least that much money in the bank.
Also, depending on where the money you currently have came from can also influence their decision. Meaning if you got a "gift" from a relative that could work against you in some buildings.
Sadly, there is no consistency when it comes to New York Real Estate and every building is different.
Feel free to reach out to me if you want to discuss this further, or if I didn't answer all of your questions.