Two GRE math questions?

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Question description

First of all, I can't use calculator during examination. I approximately have 90 seconds for each questions.

1. How do I know which one is bigger number 2^35 and 280000^2?

2. Each person at a party shook hands exactly once with each of the other people at the party. There was a total of 21 handshakes exchanged at the party. How many people are in the party?

Please explain in details and go step by step on thought process. 

Thank you! 

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