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A sprawling headquarters in Mountain View, dubbed the “Googleplex,” is a testament to the company’s explosive growth and its ambitions to become far larger.

Google owns or leases about 4.2 million square feet scattered across more than 60 buildings in Mountain View, and it hopes to build another corporate campus on a nearby NASA complex in Silicon Valley. It also signaled plans to expand in New York last year when it paid about $2 billion to buy a 15-story office spanning about 2.9 million square feet _ more space than the Empire State Building. About 2,000 Google employees currently work in that New York office.

Trying to get a job at Google is akin to trying to get into Stanford University, where Page and Brin started working on their search engine as graduate students. The company receives more than 1 million applications a year and identifies the top candidates through a rigorous screening process that analyzes SAT scores, grade-point averages and their performance on tests with such questions as: “How many different ways can you color an icosahedron with one of three colors on each face?”

The people who make it through Google’s intellectual gauntlet will likely be under intense pressure if they get hired. Management is pushing aggressively for more innovation so that the Internet giant can fend off emerging threats from smaller companies such as Facebook and Twitter.

“The opportunities are so big this year that for us to maximize them we are going to have to work quicker and we are going to have to make decisions faster,” Eustace said.

As its Internet social network grows, Facebook has become more successful at luring away Google’s workers. About 200 of Facebook’s roughly 2,000 employees used to work at Google. The defections haven’t left a big dent, given that the company hired an average of nearly 200 workers every two weeks last year.

But the recent raids by Facebook and other promising startups got Google’s attention. To retain employees, the company gave its entire work force a 10 percent raise. That move alone could increase Google’s operating expenses by about $500 million this year, based on analyst estimates. Virtually all employees also receive stock options, a benefit that turned most of the company’s early hires into multimillionaires.

Shares of Google rose $8.83, or 1.4 percent, to close at $619.91.