* They work with economies of scale. What may be viable for a startup might be useless for Google. What might be viable for Google might be absolutely disastrous for a startup.
* They use a management style that fosters innovation and learning.
The interviews can be tough, yeah, but all it takes is practice and given that you seem to have good mathematical skills, hiding a few weeks or months in the basement with an algorithms book and a laptop, should make it easy for you to pass a Google interview.